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</a>
<p style="padding: 0.5em;"><strong><a href="http://intranet.cvut.cz/cs?set_language=cs" title="ČVUT">ČVUT</a> <a href="http://www.fsv.cvut.cz/hlavni.php" title="Fakulta stavební">FSv</a></strong>
– <strong><a href="https://mat.fsv.cvut.cz/" title="Katedra matematiky">
Katedra matematiky</a></strong><br>
Thákurova 7, 166 29 Praha 6<br>
Tel.: <a href="tel:+420224354390"><strong>+420 / 224 354 390</strong></a>
</p>
</div>
<div id="eu">
<img src="./cvut1_files/opvvv.jpg"><br>
<table>
<tbody><tr><td>Příjemce:</td><td>České vysoké učení technické v Praze</td></tr>
<tr><td>Registrační číslo projektu:</td><td>CZ.02.2.69/0.0/0.0/16_015/0002382</td></tr>
<tr><td>Název projektu dle MS2014+:</td><td>Institucionální podpora Českého vysokého učení technického v Praze</td></tr>
</tbody></table>
</div>
<h2>Přijímací zkoušky z matematiky – online testování</h2>
<div id="zbyvacas" class="zbyvac1">Zbývá 67 minut</div>
<form method="post" accept-charset="utf-8" action="https://mat.fsv.cvut.cz/entrance/oprav/907b10893a2300568dc28ae20005f7bb">
<p>V následujícím online testu se na každou z 15 otázek nabízí 5 odpovědí, ale vždy <strong>jen jedna</strong> je správná.</p>
<p>Výsledek, který považujete za správný, <strong>označte v obrazci vlevo</strong>.</p>
<p>Označování odpovědí funguje ve všech prohlížečích, které podporují CSS pseudo třídu <code>:checked</code>. Pokud se Vám odpovědi neoznačují, přestože jste je vybrali, zkuste jiný prohlížeč. I pokud se Vám odpovědi neoznačují, přestože jste je vybrali, jsou vybrané a zpracují se po odeslání testu k vyhodnocení.</p>
<p>Doba vymezená na provedení testu je <strong>70 minut</strong>. Po uplynutí této doby testu je test ukončen a vyhodnocen. Test lze ukončit před uplynutím této doby. Zbývající doba je zobrazena v pravém horním rohu.</p>
<p id="java" class="cerveny" style="display: none;">Pro správnou funkci je zapotřebí mít povolený javascript.</p>
<table class="test">
<tbody><tr>
<td>
<table class="odpovedi">
<tbody><tr>
<td class="licha jednoducha"><input name="1" id="odp1a" type="radio" value="1"><label for="odp1a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="1" id="odp1b" type="radio" value="2"><label for="odp1b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="1" id="odp1c" type="radio" value="3"><label for="odp1c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="1" id="odp1d" type="radio" value="4"><label for="odp1d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="1" id="odp1e" type="radio" value="5"><label for="odp1e">e</label></td>
</tr>
</tbody></table>
1 bod
</td>
<td>
<table class="otazky">
<tbody><tr><td>1. Odchylka přímek <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-1-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>p</mi><mo>:</mo><mspace width="thinmathspace" /><msqrt><mn>3</mn></msqrt><mi>x</mi><mo>+</mo><mi>y</mi><mo>&#x2212;</mo><mn>4</mn><mo>=</mo><mn>0</mn></mrow></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1" style="width: 10.677em; display: inline-block;"><span style="display: inline-block; position: relative; width: 8.721em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.176em, 1008.7em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-2"><span class="texatom" id="MathJax-Span-3"><span class="mrow" id="MathJax-Span-4"><span class="mi" id="MathJax-Span-5" style="font-family: MathJax_Math-italic;">p</span><span class="mo" id="MathJax-Span-6" style="font-family: MathJax_Main; padding-left: 0.282em;">:</span><span class="mspace" id="MathJax-Span-7" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="msqrt" id="MathJax-Span-8" style="padding-left: 0.282em;"><span style="display: inline-block; position: relative; width: 1.344em; height: 0px;"><span style="position: absolute; clip: rect(3.188em, 1000.49em, 4.194em, -999.979em); top: -4.021em; left: 0.841em;"><span class="mrow" id="MathJax-Span-9"><span class="mn" id="MathJax-Span-10" style="font-family: MathJax_Main;">3</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.58em, 1000.49em, 3.971em, -999.979em); top: -4.524em; left: 0.841em;"><span style="font-family: MathJax_Main;">–</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.077em, 1000.88em, 4.418em, -999.979em); top: -4.077em; left: 0em;"><span style="font-family: MathJax_Main;">√</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mi" id="MathJax-Span-11" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-12" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mi" id="MathJax-Span-13" style="font-family: MathJax_Math-italic; padding-left: 0.226em;">y<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-14" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-15" style="font-family: MathJax_Main; padding-left: 0.226em;">4</span><span class="mo" id="MathJax-Span-16" style="font-family: MathJax_Main; padding-left: 0.282em;">=</span><span class="mn" id="MathJax-Span-17" style="font-family: MathJax_Main; padding-left: 0.282em;">0</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.435em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>p</mi><mo>:</mo><mspace width="thinmathspace"></mspace><msqrt><mn>3</mn></msqrt><mi>x</mi><mo>+</mo><mi>y</mi><mo>−</mo><mn>4</mn><mo>=</mo><mn>0</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-1">{p:\,\sqrt{3}x+y-4=0}</script> a <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-2-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>q</mi><mo>:</mo><mspace width="thinmathspace" /><mi>y</mi><mo>=</mo><msqrt><mn>3</mn></msqrt><mi>x</mi></mrow></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-18" style="width: 6.374em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.2em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.176em, 1005.13em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-19"><span class="texatom" id="MathJax-Span-20"><span class="mrow" id="MathJax-Span-21"><span class="mi" id="MathJax-Span-22" style="font-family: MathJax_Math-italic;">q<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-23" style="font-family: MathJax_Main; padding-left: 0.282em;">:</span><span class="mspace" id="MathJax-Span-24" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-25" style="font-family: MathJax_Math-italic; padding-left: 0.282em;">y<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-26" style="font-family: MathJax_Main; padding-left: 0.282em;">=</span><span class="msqrt" id="MathJax-Span-27" style="padding-left: 0.282em;"><span style="display: inline-block; position: relative; width: 1.344em; height: 0px;"><span style="position: absolute; clip: rect(3.188em, 1000.49em, 4.194em, -999.979em); top: -4.021em; left: 0.841em;"><span class="mrow" id="MathJax-Span-28"><span class="mn" id="MathJax-Span-29" style="font-family: MathJax_Main;">3</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.58em, 1000.49em, 3.971em, -999.979em); top: -4.524em; left: 0.841em;"><span style="font-family: MathJax_Main;">–</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.077em, 1000.88em, 4.418em, -999.979em); top: -4.077em; left: 0em;"><span style="font-family: MathJax_Main;">√</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mi" id="MathJax-Span-30" style="font-family: MathJax_Math-italic;">x</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.435em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>q</mi><mo>:</mo><mspace width="thinmathspace"></mspace><mi>y</mi><mo>=</mo><msqrt><mn>3</mn></msqrt><mi>x</mi></mrow></math></span></span><script type="math/tex" id="MathJax-Element-2">{q:\,y=\sqrt{3}x}</script> je</td></tr>
<tr><td><label for="odp1a">a) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-3-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>&#x03C0;</mi></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-31" style="width: 1.512em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.232em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.121em, 1001.21em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-32"><span class="mfrac" id="MathJax-Span-33"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.412em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-34" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-35" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mi" id="MathJax-Span-36" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>π</mi></math></span></span><script type="math/tex" id="MathJax-Element-3">\frac12\pi</script></label></td></tr>
<tr><td><label for="odp1b">b) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-4-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>3</mn></mfrac><mi>&#x03C0;</mi></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-37" style="width: 1.512em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.232em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.121em, 1001.21em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-38"><span class="mfrac" id="MathJax-Span-39"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.468em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-40" style="font-size: 70.7%; font-family: MathJax_Main;">5</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-41" style="font-size: 70.7%; font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mi" id="MathJax-Span-42" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>3</mn></mfrac><mi>π</mi></math></span></span><script type="math/tex" id="MathJax-Element-4">\frac53\pi</script></label></td></tr>
<tr><td><label for="odp1c">c) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-5-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>&#x03C0;</mi></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-43" style="width: 1.512em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.232em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.121em, 1001.21em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-44"><span class="mfrac" id="MathJax-Span-45"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.412em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-46" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-47" style="font-size: 70.7%; font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mi" id="MathJax-Span-48" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>π</mi></math></span></span><script type="math/tex" id="MathJax-Element-5">\frac13\pi</script></label></td></tr>
<tr><td><label for="odp1d">d) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-6-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>&#x03C0;</mi></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-49" style="width: 1.512em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.232em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.121em, 1001.21em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-50"><span class="mfrac" id="MathJax-Span-51"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.412em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-52" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-53" style="font-size: 70.7%; font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mi" id="MathJax-Span-54" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>π</mi></math></span></span><script type="math/tex" id="MathJax-Element-6">\frac23\pi</script></label></td></tr>
<tr><td><label for="odp1e">e) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-7-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>6</mn></mfrac><mi>&#x03C0;</mi></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-55" style="width: 1.512em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.232em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.121em, 1001.21em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-56"><span class="mfrac" id="MathJax-Span-57"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.412em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-58" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-59" style="font-size: 70.7%; font-family: MathJax_Main;">6</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mi" id="MathJax-Span-60" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>6</mn></mfrac><mi>π</mi></math></span></span><script type="math/tex" id="MathJax-Element-7">\frac16\pi</script></label></td></tr>
</tbody></table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tbody><tr>
<td class="licha dvojita"><input name="2" id="odp2a" type="radio" value="1"><label for="odp2a">a</label></td>
<td> </td>
<td class="licha dvojita"><input name="2" id="odp2b" type="radio" value="2"><label for="odp2b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha dvojita"><input name="2" id="odp2c" type="radio" value="3"><label for="odp2c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha dvojita"><input name="2" id="odp2d" type="radio" value="4"><label for="odp2d">d</label></td>
<td> </td>
<td class="licha dvojita"><input name="2" id="odp2e" type="radio" value="5"><label for="odp2e">e</label></td>
</tr>
</tbody></table>
2 body
</td>
<td>
<table class="otazky">
<tbody><tr><td>2. Rovnice <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-8-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><msup><mi>x</mi><mn>2</mn></msup><mo>&#x2212;</mo><mn>2</mn><msup><mi>y</mi><mn>2</mn></msup><mo>&#x2212;</mo><mn>4</mn><mi>x</mi><mo>&#x2212;</mo><mn>16</mn><mi>y</mi><mo>&#x2212;</mo><mn>28</mn><mo>=</mo><mn>0</mn></mrow></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-61" style="width: 15.651em; display: inline-block;"><span style="display: inline-block; position: relative; width: 12.801em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.176em, 1012.78em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-62"><span class="texatom" id="MathJax-Span-63"><span class="mrow" id="MathJax-Span-64"><span class="msubsup" id="MathJax-Span-65"><span style="display: inline-block; position: relative; width: 1.009em; height: 0px;"><span style="position: absolute; clip: rect(3.412em, 1000.54em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-66" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.356em; left: 0.562em;"><span class="mn" id="MathJax-Span-67" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-68" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-69" style="font-family: MathJax_Main; padding-left: 0.226em;">2</span><span class="msubsup" id="MathJax-Span-70"><span style="display: inline-block; position: relative; width: 0.953em; height: 0px;"><span style="position: absolute; clip: rect(3.412em, 1000.49em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-71" style="font-family: MathJax_Math-italic;">y<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.356em; left: 0.562em;"><span class="mn" id="MathJax-Span-72" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-73" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-74" style="font-family: MathJax_Main; padding-left: 0.226em;">4</span><span class="mi" id="MathJax-Span-75" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-76" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-77" style="font-family: MathJax_Main; padding-left: 0.226em;">16</span><span class="mi" id="MathJax-Span-78" style="font-family: MathJax_Math-italic;">y<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-79" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-80" style="font-family: MathJax_Main; padding-left: 0.226em;">28</span><span class="mo" id="MathJax-Span-81" style="font-family: MathJax_Main; padding-left: 0.282em;">=</span><span class="mn" id="MathJax-Span-82" style="font-family: MathJax_Main; padding-left: 0.282em;">0</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.435em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><msup><mi>y</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>−</mo><mn>16</mn><mi>y</mi><mo>−</mo><mn>28</mn><mo>=</mo><mn>0</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-8">{x^2-2y^2-4x-16y-28=0}</script> je analytickým vyjádřením</td></tr>
<tr><td><label for="odp2a">a) jedné přímky</label></td></tr>
<tr><td><label for="odp2b">b) dvojice rovnoběžných přímek</label></td></tr>
<tr><td><label for="odp2c">c) hyperboly</label></td></tr>
<tr><td><label for="odp2d">d) kružnice</label></td></tr>
<tr><td><label for="odp2e">e) dvojice různoběžných přímek</label></td></tr>
</tbody></table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tbody><tr>
<td class="licha jednoducha"><input name="3" id="odp3a" type="radio" value="1"><label for="odp3a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="3" id="odp3b" type="radio" value="2"><label for="odp3b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="3" id="odp3c" type="radio" value="3"><label for="odp3c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="3" id="odp3d" type="radio" value="4"><label for="odp3d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="3" id="odp3e" type="radio" value="5"><label for="odp3e">e</label></td>
</tr>
</tbody></table>
1 bod
</td>
<td>
<table class="otazky">
<tbody><tr><td>3. Člen <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-9-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>3</mn></msub></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-83" style="width: 1.176em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.953em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.568em, 1000.93em, 2.518em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-84"><span class="msubsup" id="MathJax-Span-85"><span style="display: inline-block; position: relative; width: 0.953em; height: 0px;"><span style="position: absolute; clip: rect(3.412em, 1000.49em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-86" style="font-family: MathJax_Math-italic;">a</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -3.853em; left: 0.506em;"><span class="mn" id="MathJax-Span-87" style="font-size: 70.7%; font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.269em; border-left: 0px solid; width: 0px; height: 0.89em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mn>3</mn></msub></math></span></span><script type="math/tex" id="MathJax-Element-9">a_3</script> v aritmetické posloupnosti, kde člen <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-10-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msub><mo>=</mo><mn>25</mn></mrow></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-88" style="width: 4.474em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.635em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1003.56em, 2.518em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-89"><span class="texatom" id="MathJax-Span-90"><span class="mrow" id="MathJax-Span-91"><span class="msubsup" id="MathJax-Span-92"><span style="display: inline-block; position: relative; width: 1.288em; height: 0px;"><span style="position: absolute; clip: rect(3.412em, 1000.49em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-93" style="font-family: MathJax_Math-italic;">a</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -3.853em; left: 0.506em;"><span class="texatom" id="MathJax-Span-94"><span class="mrow" id="MathJax-Span-95"><span class="mn" id="MathJax-Span-96" style="font-size: 70.7%; font-family: MathJax_Main;">10</span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-97" style="font-family: MathJax_Main; padding-left: 0.282em;">=</span><span class="mn" id="MathJax-Span-98" style="font-family: MathJax_Main; padding-left: 0.282em;">25</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.269em; border-left: 0px solid; width: 0px; height: 1.163em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mn>10</mn></mrow></msub><mo>=</mo><mn>25</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-10">{a_{10}=25}</script> a diference <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-11-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>d</mi><mo>=</mo><mn>4</mn></mrow></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-99" style="width: 2.909em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.35em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1002.33em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-100"><span class="texatom" id="MathJax-Span-101"><span class="mrow" id="MathJax-Span-102"><span class="mi" id="MathJax-Span-103" style="font-family: MathJax_Math-italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-104" style="font-family: MathJax_Main; padding-left: 0.282em;">=</span><span class="mn" id="MathJax-Span-105" style="font-family: MathJax_Main; padding-left: 0.282em;">4</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 1.026em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>d</mi><mo>=</mo><mn>4</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-11">{d=4}</script>, je</td></tr>
<tr><td><label for="odp3a">a) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-12-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2212;</mo><mn>3</mn></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-106" style="width: 1.568em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.288em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1001.27em, 2.406em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-107"><span class="mo" id="MathJax-Span-108" style="font-family: MathJax_Main;">−</span><span class="mn" id="MathJax-Span-109" style="font-family: MathJax_Main;">3</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.133em; border-left: 0px solid; width: 0px; height: 1.026em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mn>3</mn></math></span></span><script type="math/tex" id="MathJax-Element-12">-3</script></label></td></tr>
<tr><td><label for="odp3b">b) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-13-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-110" style="width: 0.618em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.506em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1000.43em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-111"><span class="mn" id="MathJax-Span-112" style="font-family: MathJax_Main;">1</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 0.958em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span></span><script type="math/tex" id="MathJax-Element-13">1</script></label></td></tr>
<tr><td><label for="odp3c">c) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-14-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2212;</mo><mn>1</mn></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-113" style="width: 1.568em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.288em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1001.21em, 2.406em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-114"><span class="mo" id="MathJax-Span-115" style="font-family: MathJax_Main;">−</span><span class="mn" id="MathJax-Span-116" style="font-family: MathJax_Main;">1</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.133em; border-left: 0px solid; width: 0px; height: 1.026em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mn>1</mn></math></span></span><script type="math/tex" id="MathJax-Element-14">-1</script></label></td></tr>
<tr><td><label for="odp3d">d) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-15-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2212;</mo><mn>7</mn></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-117" style="width: 1.568em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.288em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1001.27em, 2.406em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-118"><span class="mo" id="MathJax-Span-119" style="font-family: MathJax_Main;">−</span><span class="mn" id="MathJax-Span-120" style="font-family: MathJax_Main;">7</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.133em; border-left: 0px solid; width: 0px; height: 1.094em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mn>7</mn></math></span></span><script type="math/tex" id="MathJax-Element-15">-7</script></label></td></tr>
<tr><td><label for="odp3e">e) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-16-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2212;</mo><mn>5</mn></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-121" style="width: 1.568em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.288em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1001.21em, 2.406em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-122"><span class="mo" id="MathJax-Span-123" style="font-family: MathJax_Main;">−</span><span class="mn" id="MathJax-Span-124" style="font-family: MathJax_Main;">5</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.133em; border-left: 0px solid; width: 0px; height: 1.026em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mn>5</mn></math></span></span><script type="math/tex" id="MathJax-Element-16">-5</script></label></td></tr>
</tbody></table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tbody><tr>
<td class="licha jednoducha"><input name="4" id="odp4a" type="radio" value="1"><label for="odp4a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="4" id="odp4b" type="radio" value="2"><label for="odp4b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="4" id="odp4c" type="radio" value="3"><label for="odp4c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="4" id="odp4d" type="radio" value="4"><label for="odp4d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="4" id="odp4e" type="radio" value="5"><label for="odp4e">e</label></td>
</tr>
</tbody></table>
1 bod
</td>
<td>
<table class="otazky">
<tbody><tr><td>4. Jestliže <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-17-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-OP"><mtext>tg</mtext><mspace width="thinmathspace" /></mrow></mrow><mi>&#x03B1;</mi><mo>=</mo><mn>1</mn></mrow></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-125" style="width: 4.306em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.524em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1003.45em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-126"><span class="texatom" id="MathJax-Span-127"><span class="mrow" id="MathJax-Span-128"><span class="texatom" id="MathJax-Span-129"><span class="mrow" id="MathJax-Span-130"><span class="texatom" id="MathJax-Span-131"><span class="mrow" id="MathJax-Span-132"><span class="mtext" id="MathJax-Span-133" style="font-family: MathJax_Main;">tg</span><span class="mspace" id="MathJax-Span-134" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span></span></span></span></span><span class="mi" id="MathJax-Span-135" style="font-family: MathJax_Math-italic;">α</span><span class="mo" id="MathJax-Span-136" style="font-family: MathJax_Main; padding-left: 0.282em;">=</span><span class="mn" id="MathJax-Span-137" style="font-family: MathJax_Main; padding-left: 0.282em;">1</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.231em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-OP"><mtext>tg</mtext><mspace width="thinmathspace"></mspace></mrow></mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-17">{\tg\alpha=1}</script>, pak <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-18-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo>&#x2061;</mo><mn>2</mn><mi>&#x03B1;</mi></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-138" style="width: 3.077em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.518em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1002.5em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-139"><span class="mi" id="MathJax-Span-140" style="font-family: MathJax_Main;">sin</span><span class="mo" id="MathJax-Span-141"></span><span class="mn" id="MathJax-Span-142" style="font-family: MathJax_Main; padding-left: 0.17em;">2</span><span class="mi" id="MathJax-Span-143" style="font-family: MathJax_Math-italic;">α</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 0.958em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo></mo><mn>2</mn><mi>α</mi></math></span></span><script type="math/tex" id="MathJax-Element-18">\sin2\alpha</script> se rovná číslu</td></tr>
<tr><td><label for="odp4a">a) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-19-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2212;</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-144" style="width: 2.518em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.071em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.897em, 1002.05em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-145"><span class="mo" id="MathJax-Span-146" style="font-family: MathJax_Main;">−</span><span class="mfrac" id="MathJax-Span-147"><span style="display: inline-block; position: relative; width: 1.065em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.3em, 1000.93em, 4.306em, -999.979em); top: -4.58em; left: 50%; margin-left: -0.444em;"><span class="msqrt" id="MathJax-Span-148"><span style="display: inline-block; position: relative; width: 0.953em; height: 0px;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.021em; left: 0.618em;"><span class="mrow" id="MathJax-Span-149"><span class="mn" id="MathJax-Span-150" style="font-size: 70.7%; font-family: MathJax_Main;">2</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.953em, 1000.38em, 1.288em, -999.979em); top: -1.674em; left: 0.618em;"><span style="display: inline-block; overflow: hidden; vertical-align: -0.053em; border-top: 1.3px solid; width: 0.338em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span><span style="position: absolute; clip: rect(3.3em, 1000.6em, 4.362em, -999.979em); top: -4.021em; left: 0em;"><span><span style="font-size: 70.7%; font-family: MathJax_Main;">√</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-151" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1001.05em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.065em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.981em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></span></span><script type="math/tex" id="MathJax-Element-19">-\frac{\sqrt2}{2}</script></label></td></tr>
<tr><td><label for="odp4b">b) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-20-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-152" style="width: 0.618em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.506em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1000.43em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-153"><span class="mn" id="MathJax-Span-154" style="font-family: MathJax_Main;">1</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 0.958em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span></span><script type="math/tex" id="MathJax-Element-20">1</script></label></td></tr>
<tr><td><label for="odp4c">c) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-21-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2212;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-155" style="width: 1.791em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.456em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.121em, 1001.44em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-156"><span class="mo" id="MathJax-Span-157" style="font-family: MathJax_Main;">−</span><span class="mfrac" id="MathJax-Span-158"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.412em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-159" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-160" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></span></span><script type="math/tex" id="MathJax-Element-21">-\frac12</script></label></td></tr>
<tr><td><label for="odp4d">d) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-22-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-161" style="width: 0.618em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.506em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1000.49em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-162"><span class="mn" id="MathJax-Span-163" style="font-family: MathJax_Main;">0</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 0.958em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-22">0</script></label></td></tr>
<tr><td><label for="odp4e">e) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-23-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-164" style="width: 1.568em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.288em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.897em, 1001.27em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-165"><span class="mfrac" id="MathJax-Span-166"><span style="display: inline-block; position: relative; width: 1.065em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.3em, 1000.93em, 4.306em, -999.979em); top: -4.58em; left: 50%; margin-left: -0.444em;"><span class="msqrt" id="MathJax-Span-167"><span style="display: inline-block; position: relative; width: 0.953em; height: 0px;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.021em; left: 0.618em;"><span class="mrow" id="MathJax-Span-168"><span class="mn" id="MathJax-Span-169" style="font-size: 70.7%; font-family: MathJax_Main;">2</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.953em, 1000.38em, 1.288em, -999.979em); top: -1.674em; left: 0.618em;"><span style="display: inline-block; overflow: hidden; vertical-align: -0.053em; border-top: 1.3px solid; width: 0.338em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span><span style="position: absolute; clip: rect(3.3em, 1000.6em, 4.362em, -999.979em); top: -4.021em; left: 0em;"><span><span style="font-size: 70.7%; font-family: MathJax_Main;">√</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-170" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1001.05em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.065em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.981em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></span></span><script type="math/tex" id="MathJax-Element-23">\frac{\sqrt2}{2}</script></label></td></tr>
</tbody></table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tbody><tr>
<td class="licha dvojita"><input name="5" id="odp5a" type="radio" value="1"><label for="odp5a">a</label></td>
<td> </td>
<td class="licha dvojita"><input name="5" id="odp5b" type="radio" value="2"><label for="odp5b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha dvojita"><input name="5" id="odp5c" type="radio" value="3"><label for="odp5c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha dvojita"><input name="5" id="odp5d" type="radio" value="4"><label for="odp5d">d</label></td>
<td> </td>
<td class="licha dvojita"><input name="5" id="odp5e" type="radio" value="5"><label for="odp5e">e</label></td>
</tr>
</tbody></table>
2 body
</td>
<td>
<table class="otazky">
<tbody><tr><td>5. Objem komolého pravidelného čtyřbokého jehlanu, který má hranu dolní podstavy <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-24-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mspace width="thinmathspace" /></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-171" style="width: 1.456em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.176em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1001.16em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-172"><span class="mn" id="MathJax-Span-173" style="font-family: MathJax_Main;">10</span><span class="mspace" id="MathJax-Span-174" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 0.958em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mspace width="thinmathspace"></mspace></math></span></span><script type="math/tex" id="MathJax-Element-24">10\,</script>m, hranu horní podstavy <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-25-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mspace width="thinmathspace" /></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-175" style="width: 0.841em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.673em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1000.65em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-176"><span class="mn" id="MathJax-Span-177" style="font-family: MathJax_Main;">8</span><span class="mspace" id="MathJax-Span-178" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 0.958em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mspace width="thinmathspace"></mspace></math></span></span><script type="math/tex" id="MathJax-Element-25">8\,</script>m a odchylku bočních stěn od podstavy <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-26-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>45</mn><mo>&#x2218;</mo></msup></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-179" style="width: 1.791em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.456em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1001.44em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-180"><span class="msubsup" id="MathJax-Span-181"><span style="display: inline-block; position: relative; width: 1.456em; height: 0px;"><span style="position: absolute; clip: rect(3.188em, 1000.93em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mn" id="MathJax-Span-182" style="font-family: MathJax_Main;">45</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.412em; left: 1.009em;"><span class="mo" id="MathJax-Span-183" style="font-size: 70.7%; font-family: MathJax_Main;">∘</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 1.026em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>45</mn><mo>∘</mo></msup></math></span></span><script type="math/tex" id="MathJax-Element-26">45^\circ</script>, je</td></tr>
<tr><td><label for="odp5a">a) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-27-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>244</mn><mn>3</mn></mfrac></mstyle></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-184" style="width: 2.294em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.847em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.673em, 1001.83em, 3.077em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-185"><span class="mstyle" id="MathJax-Span-186"><span class="mrow" id="MathJax-Span-187"><span class="mfrac" id="MathJax-Span-188"><span style="display: inline-block; position: relative; width: 1.624em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.188em, 1001.49em, 4.194em, -999.979em); top: -4.692em; left: 50%; margin-left: -0.724em;"><span class="mn" id="MathJax-Span-189" style="font-family: MathJax_Main;">244</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.188em, 1000.49em, 4.194em, -999.979em); top: -3.35em; left: 50%; margin-left: -0.221em;"><span class="mn" id="MathJax-Span-190" style="font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1001.61em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.624em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.951em; border-left: 0px solid; width: 0px; height: 2.663em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>244</mn><mn>3</mn></mfrac></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-27">\dfrac{244}3</script> m<span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-28-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>3</mn></msup></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-191" style="width: 0.562em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.176em, 1000.43em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-192"><span class="msubsup" id="MathJax-Span-193"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px;"><span style="position: absolute; clip: rect(3.859em, 999.984em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-194"></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.356em; left: 0em;"><span class="mn" id="MathJax-Span-195" style="font-size: 70.7%; font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 1.163em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>3</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-28">^3</script></label></td></tr>
<tr><td><label for="odp5b">b) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-29-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>245</mn><mn>3</mn></mfrac></mstyle></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-196" style="width: 2.294em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.847em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.673em, 1001.83em, 3.077em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-197"><span class="mstyle" id="MathJax-Span-198"><span class="mrow" id="MathJax-Span-199"><span class="mfrac" id="MathJax-Span-200"><span style="display: inline-block; position: relative; width: 1.624em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.188em, 1001.44em, 4.194em, -999.979em); top: -4.692em; left: 50%; margin-left: -0.724em;"><span class="mn" id="MathJax-Span-201" style="font-family: MathJax_Main;">245</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.188em, 1000.49em, 4.194em, -999.979em); top: -3.35em; left: 50%; margin-left: -0.221em;"><span class="mn" id="MathJax-Span-202" style="font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1001.61em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.624em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.951em; border-left: 0px solid; width: 0px; height: 2.663em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>245</mn><mn>3</mn></mfrac></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-29">\dfrac{245}3</script> m<span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-30-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>3</mn></msup></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-203" style="width: 0.562em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.176em, 1000.43em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-204"><span class="msubsup" id="MathJax-Span-205"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px;"><span style="position: absolute; clip: rect(3.859em, 999.984em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-206"></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.356em; left: 0em;"><span class="mn" id="MathJax-Span-207" style="font-size: 70.7%; font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 1.163em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>3</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-30">^3</script></label></td></tr>
<tr><td><label for="odp5c">c) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-31-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>145</mn><mn>3</mn></mfrac></mstyle></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-208" style="width: 2.294em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.847em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.673em, 1001.83em, 3.077em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-209"><span class="mstyle" id="MathJax-Span-210"><span class="mrow" id="MathJax-Span-211"><span class="mfrac" id="MathJax-Span-212"><span style="display: inline-block; position: relative; width: 1.624em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.188em, 1001.44em, 4.194em, -999.979em); top: -4.692em; left: 50%; margin-left: -0.724em;"><span class="mn" id="MathJax-Span-213" style="font-family: MathJax_Main;">145</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.188em, 1000.49em, 4.194em, -999.979em); top: -3.35em; left: 50%; margin-left: -0.221em;"><span class="mn" id="MathJax-Span-214" style="font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1001.61em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.624em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.951em; border-left: 0px solid; width: 0px; height: 2.663em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>145</mn><mn>3</mn></mfrac></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-31">\dfrac{145}3</script> m<span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-32-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>3</mn></msup></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-215" style="width: 0.562em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.176em, 1000.43em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-216"><span class="msubsup" id="MathJax-Span-217"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px;"><span style="position: absolute; clip: rect(3.859em, 999.984em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-218"></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.356em; left: 0em;"><span class="mn" id="MathJax-Span-219" style="font-size: 70.7%; font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 1.163em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>3</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-32">^3</script></label></td></tr>
<tr><td><label for="odp5d">d) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-33-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>144</mn><mn>3</mn></mfrac></mstyle></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-220" style="width: 2.294em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.847em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.673em, 1001.83em, 3.077em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-221"><span class="mstyle" id="MathJax-Span-222"><span class="mrow" id="MathJax-Span-223"><span class="mfrac" id="MathJax-Span-224"><span style="display: inline-block; position: relative; width: 1.624em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.188em, 1001.49em, 4.194em, -999.979em); top: -4.692em; left: 50%; margin-left: -0.724em;"><span class="mn" id="MathJax-Span-225" style="font-family: MathJax_Main;">144</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.188em, 1000.49em, 4.194em, -999.979em); top: -3.35em; left: 50%; margin-left: -0.221em;"><span class="mn" id="MathJax-Span-226" style="font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1001.61em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.624em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.951em; border-left: 0px solid; width: 0px; height: 2.663em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>144</mn><mn>3</mn></mfrac></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-33">\dfrac{144}3</script> m<span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-34-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>3</mn></msup></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-227" style="width: 0.562em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.176em, 1000.43em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-228"><span class="msubsup" id="MathJax-Span-229"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px;"><span style="position: absolute; clip: rect(3.859em, 999.984em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-230"></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.356em; left: 0em;"><span class="mn" id="MathJax-Span-231" style="font-size: 70.7%; font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 1.163em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>3</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-34">^3</script></label></td></tr>
<tr><td><label for="odp5e">e) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-35-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>245</mn><mn>4</mn></mfrac></mstyle></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-232" style="width: 2.294em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.847em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.673em, 1001.83em, 3.021em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-233"><span class="mstyle" id="MathJax-Span-234"><span class="mrow" id="MathJax-Span-235"><span class="mfrac" id="MathJax-Span-236"><span style="display: inline-block; position: relative; width: 1.624em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.188em, 1001.44em, 4.194em, -999.979em); top: -4.692em; left: 50%; margin-left: -0.724em;"><span class="mn" id="MathJax-Span-237" style="font-family: MathJax_Main;">245</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.188em, 1000.49em, 4.194em, -999.979em); top: -3.35em; left: 50%; margin-left: -0.221em;"><span class="mn" id="MathJax-Span-238" style="font-family: MathJax_Main;">4</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1001.61em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.624em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.883em; border-left: 0px solid; width: 0px; height: 2.594em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>245</mn><mn>4</mn></mfrac></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-35">\dfrac{245}4</script> m<span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-36-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>3</mn></msup></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-239" style="width: 0.562em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.176em, 1000.43em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-240"><span class="msubsup" id="MathJax-Span-241"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px;"><span style="position: absolute; clip: rect(3.859em, 999.984em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-242"></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.356em; left: 0em;"><span class="mn" id="MathJax-Span-243" style="font-size: 70.7%; font-family: MathJax_Main;">3</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 1.163em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>3</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-36">^3</script></label></td></tr>
</tbody></table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tbody><tr>
<td class="licha jednoducha"><input name="6" id="odp6a" type="radio" value="1"><label for="odp6a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="6" id="odp6b" type="radio" value="2"><label for="odp6b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="6" id="odp6c" type="radio" value="3"><label for="odp6c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="6" id="odp6d" type="radio" value="4"><label for="odp6d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="6" id="odp6e" type="radio" value="5"><label for="odp6e">e</label></td>
</tr>
</tbody></table>
1 bod
</td>
<td>
<table class="otazky">
<tbody><tr><td>6. Množinou všech řešení nerovnice <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-37-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mn>3</mn><mo>&#x2212;</mo><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mrow></mfrac></mstyle><mo>&#x2264;</mo><mn>2</mn></mrow></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-244" style="width: 6.15em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.033em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.673em, 1004.96em, 3.356em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-245"><span class="texatom" id="MathJax-Span-246"><span class="mrow" id="MathJax-Span-247"><span class="mstyle" id="MathJax-Span-248"><span class="mrow" id="MathJax-Span-249"><span class="mfrac" id="MathJax-Span-250"><span style="display: inline-block; position: relative; width: 2.965em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.188em, 1000.43em, 4.194em, -999.979em); top: -4.692em; left: 50%; margin-left: -0.221em;"><span class="mn" id="MathJax-Span-251" style="font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.132em, 1002.72em, 4.418em, -999.979em); top: -3.295em; left: 50%; margin-left: -1.45em;"><span class="mrow" id="MathJax-Span-252"><span class="texatom" id="MathJax-Span-253"><span class="mrow" id="MathJax-Span-254"><span class="mo" id="MathJax-Span-255" style="font-family: MathJax_Main;">|</span></span></span><span class="mn" id="MathJax-Span-256" style="font-family: MathJax_Main;">3</span><span class="mo" id="MathJax-Span-257" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mi" id="MathJax-Span-258" style="font-family: MathJax_Math-italic; padding-left: 0.226em;">x</span><span class="texatom" id="MathJax-Span-259"><span class="mrow" id="MathJax-Span-260"><span class="mo" id="MathJax-Span-261" style="font-family: MathJax_Main;">|</span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1003em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 2.965em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-262" style="font-family: MathJax_Main; padding-left: 0.282em;">≤</span><span class="mn" id="MathJax-Span-263" style="font-family: MathJax_Main; padding-left: 0.282em;">2</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.292em; border-left: 0px solid; width: 0px; height: 3.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mn>3</mn><mo>−</mo><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mrow></mfrac></mstyle><mo>≤</mo><mn>2</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-37">{\dfrac1{|3-x|}\le2}</script> s neznámou <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-38-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>x</mi><mo>&#x2208;</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">R</mi></mrow></mrow></mrow></math>" role="presentation"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-264" style="width: 3.077em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.518em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.624em, 1002.5em, 2.685em, -999.979em); top: -2.456em; left: 0em;"><span class="mrow" id="MathJax-Span-265"><span class="texatom" id="MathJax-Span-266"><span class="mrow" id="MathJax-Span-267"><span class="mi" id="MathJax-Span-268" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-269" style="font-family: MathJax_Main; padding-left: 0.282em;">∈</span><span class="texatom" id="MathJax-Span-270" style="padding-left: 0.282em;"><span class="mrow" id="MathJax-Span-271"><span class="texatom" id="MathJax-Span-272"><span class="mrow" id="MathJax-Span-273"><span class="mi" id="MathJax-Span-274" style="font-family: MathJax_AMS;">R</span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.462em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.133em; border-left: 0px solid; width: 0px; height: 1.026em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>x</mi><mo>∈</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">R</mi></mrow></mrow></mrow></math></span></span><script type="math/tex" id="MathJax-Element-38">{x\in\R}</script> je</td></tr>
<tr><td><label for="odp6a">a) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-39-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mo>&#x2212;</mo><mi mathvariant="normal">&#x221E;</mi><mo>,</mo><mspace width="thinmathspace" /><mn>3</mn><mo stretchy="false">)</mo><mo>&#x222A;</mo><mo stretchy="false">(</mo><mn>3</mn><mo>,</mo><mspace width="thinmathspace" /><mi mathvariant="normal">&#x221E;</mi><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-275" style="width: 9.448em; display: inline-block;"><span style="display: inline-block; position: relative; width: 7.715em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1007.64em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-276"><span class="mo" id="MathJax-Span-277" style="font-family: MathJax_Main;">(</span><span class="mo" id="MathJax-Span-278" style="font-family: MathJax_Main;">−</span><span class="mi" id="MathJax-Span-279" style="font-family: MathJax_Main;">∞</span><span class="mo" id="MathJax-Span-280" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-281" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-282" style="font-family: MathJax_Main; padding-left: 0.17em;">3</span><span class="mo" id="MathJax-Span-283" style="font-family: MathJax_Main;">)</span><span class="mo" id="MathJax-Span-284" style="font-family: MathJax_Main; padding-left: 0.226em;">∪</span><span class="mo" id="MathJax-Span-285" style="font-family: MathJax_Main; padding-left: 0.226em;">(</span><span class="mn" id="MathJax-Span-286" style="font-family: MathJax_Main;">3</span><span class="mo" id="MathJax-Span-287" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-288" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-289" style="font-family: MathJax_Main; padding-left: 0.17em;">∞</span><span class="mo" id="MathJax-Span-290" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mo>−</mo><mi mathvariant="normal">∞</mi><mo>,</mo><mspace width="thinmathspace"></mspace><mn>3</mn><mo stretchy="false">)</mo><mo>∪</mo><mo stretchy="false">(</mo><mn>3</mn><mo>,</mo><mspace width="thinmathspace"></mspace><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-39">(-\infty,\,3)\cup(3,\,\infty)</script></label></td></tr>
<tr><td><label for="odp6b">b) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-40-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mo>&#x2212;</mo><mi mathvariant="normal">&#x221E;</mi><mo>,</mo><mspace width="thinmathspace" /><mfrac><mn>5</mn><mn>2</mn></mfrac><mo fence="false" stretchy="false">&#x27E9;</mo><mo>&#x222A;</mo><mo fence="false" stretchy="false">&#x27E8;</mo><mfrac><mn>7</mn><mn>2</mn></mfrac><mo>,</mo><mspace width="thinmathspace" /><mi mathvariant="normal">&#x221E;</mi><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-291" style="width: 9.839em; display: inline-block;"><span style="display: inline-block; position: relative; width: 8.05em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.121em, 1007.98em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-292"><span class="mo" id="MathJax-Span-293" style="font-family: MathJax_Main;">(</span><span class="mo" id="MathJax-Span-294" style="font-family: MathJax_Main;">−</span><span class="mi" id="MathJax-Span-295" style="font-family: MathJax_Main;">∞</span><span class="mo" id="MathJax-Span-296" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-297" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mfrac" id="MathJax-Span-298" style="padding-left: 0.17em;"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.468em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-299" style="font-size: 70.7%; font-family: MathJax_Main;">5</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-300" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mo" id="MathJax-Span-301" style="font-family: MathJax_Main;">⟩</span><span class="mo" id="MathJax-Span-302" style="font-family: MathJax_Main; padding-left: 0.226em;">∪</span><span class="mo" id="MathJax-Span-303" style="font-family: MathJax_Main; padding-left: 0.226em;">⟨</span><span class="mfrac" id="MathJax-Span-304"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.356em, 1000.32em, 4.194em, -999.979em); top: -4.468em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-305" style="font-size: 70.7%; font-family: MathJax_Main;">7</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-306" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mo" id="MathJax-Span-307" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-308" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-309" style="font-family: MathJax_Main; padding-left: 0.17em;">∞</span><span class="mo" id="MathJax-Span-310" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mo>−</mo><mi mathvariant="normal">∞</mi><mo>,</mo><mspace width="thinmathspace"></mspace><mfrac><mn>5</mn><mn>2</mn></mfrac><mo fence="false" stretchy="false">⟩</mo><mo>∪</mo><mo fence="false" stretchy="false">⟨</mo><mfrac><mn>7</mn><mn>2</mn></mfrac><mo>,</mo><mspace width="thinmathspace"></mspace><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-40">(-\infty,\,\frac52\rangle \cup\langle \frac72,\,\infty)</script></label></td></tr>
<tr><td><label for="odp6c">c) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-41-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace" /><mn>5</mn><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-311" style="width: 2.965em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.406em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1002.33em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-312"><span class="mo" id="MathJax-Span-313" style="font-family: MathJax_Main;">(</span><span class="mn" id="MathJax-Span-314" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-315" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-316" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-317" style="font-family: MathJax_Main; padding-left: 0.17em;">5</span><span class="mo" id="MathJax-Span-318" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace"></mspace><mn>5</mn><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-41">(1,\,5)</script></label></td></tr>
<tr><td><label for="odp6d">d) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-42-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">&#x27E8;</mo><mfrac><mn>7</mn><mn>2</mn></mfrac><mo>,</mo><mspace width="thinmathspace" /><mi mathvariant="normal">&#x221E;</mi><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-319" style="width: 3.747em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.077em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.121em, 1003em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-320"><span class="mo" id="MathJax-Span-321" style="font-family: MathJax_Main;">⟨</span><span class="mfrac" id="MathJax-Span-322"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.356em, 1000.32em, 4.194em, -999.979em); top: -4.468em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-323" style="font-size: 70.7%; font-family: MathJax_Main;">7</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-324" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mo" id="MathJax-Span-325" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-326" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-327" style="font-family: MathJax_Main; padding-left: 0.17em;">∞</span><span class="mo" id="MathJax-Span-328" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">⟨</mo><mfrac><mn>7</mn><mn>2</mn></mfrac><mo>,</mo><mspace width="thinmathspace"></mspace><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-42">\langle \frac72,\,\infty)</script></label></td></tr>
<tr><td><label for="odp6e">e) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-43-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">&#x27E8;</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace" /><mn>3</mn><mo stretchy="false">)</mo><mo>&#x222A;</mo><mo stretchy="false">(</mo><mn>3</mn><mo>,</mo><mspace width="thinmathspace" /><mn>5</mn><mo fence="false" stretchy="false">&#x27E9;</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-329" style="width: 7.268em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.927em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1005.8em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-330"><span class="mo" id="MathJax-Span-331" style="font-family: MathJax_Main;">⟨</span><span class="mn" id="MathJax-Span-332" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-333" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-334" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-335" style="font-family: MathJax_Main; padding-left: 0.17em;">3</span><span class="mo" id="MathJax-Span-336" style="font-family: MathJax_Main;">)</span><span class="mo" id="MathJax-Span-337" style="font-family: MathJax_Main; padding-left: 0.226em;">∪</span><span class="mo" id="MathJax-Span-338" style="font-family: MathJax_Main; padding-left: 0.226em;">(</span><span class="mn" id="MathJax-Span-339" style="font-family: MathJax_Main;">3</span><span class="mo" id="MathJax-Span-340" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-341" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-342" style="font-family: MathJax_Main; padding-left: 0.17em;">5</span><span class="mo" id="MathJax-Span-343" style="font-family: MathJax_Main;">⟩</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">⟨</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace"></mspace><mn>3</mn><mo stretchy="false">)</mo><mo>∪</mo><mo stretchy="false">(</mo><mn>3</mn><mo>,</mo><mspace width="thinmathspace"></mspace><mn>5</mn><mo fence="false" stretchy="false">⟩</mo></math></span></span><script type="math/tex" id="MathJax-Element-43">\langle 1,\,3)\cup(3,\,5\rangle </script></label></td></tr>
</tbody></table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tbody><tr>
<td class="licha jednoducha"><input name="7" id="odp7a" type="radio" value="1"><label for="odp7a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="7" id="odp7b" type="radio" value="2"><label for="odp7b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="7" id="odp7c" type="radio" value="3"><label for="odp7c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="7" id="odp7d" type="radio" value="4"><label for="odp7d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="7" id="odp7e" type="radio" value="5"><label for="odp7e">e</label></td>
</tr>
</tbody></table>
1 bod
</td>
<td>
<table class="otazky">
<tbody><tr><td>7. Algebraický tvar komplexního čísla <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-44-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>z</mi><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>2</mn><mrow><mn>1</mn><mo>+</mo><msup><mrow class="MJX-TeXAtom-ORD"><mtext>i</mtext></mrow><mn>7</mn></msup></mrow></mfrac></mstyle></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-344" style="width: 5.591em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.586em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.673em, 1004.57em, 3.3em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-345"><span class="texatom" id="MathJax-Span-346"><span class="mrow" id="MathJax-Span-347"><span class="mi" id="MathJax-Span-348" style="font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-349" style="font-family: MathJax_Main; padding-left: 0.282em;">=</span><span class="mstyle" id="MathJax-Span-350" style="padding-left: 0.282em;"><span class="mrow" id="MathJax-Span-351"><span class="mfrac" id="MathJax-Span-352"><span style="display: inline-block; position: relative; width: 2.574em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.188em, 1000.43em, 4.194em, -999.979em); top: -4.692em; left: 50%; margin-left: -0.221em;"><span class="mn" id="MathJax-Span-353" style="font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(2.965em, 1002.44em, 4.25em, -999.979em); top: -3.183em; left: 50%; margin-left: -1.227em;"><span class="mrow" id="MathJax-Span-354"><span class="mn" id="MathJax-Span-355" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-356" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="msubsup" id="MathJax-Span-357" style="padding-left: 0.226em;"><span style="display: inline-block; position: relative; width: 0.729em; height: 0px;"><span style="position: absolute; clip: rect(3.188em, 1000.26em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="texatom" id="MathJax-Span-358"><span class="mrow" id="MathJax-Span-359"><span class="mtext" id="MathJax-Span-360" style="font-family: MathJax_Main;">i</span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.412em; left: 0.282em;"><span class="mn" id="MathJax-Span-361" style="font-size: 70.7%; font-family: MathJax_Main;">7</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1002.55em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 2.574em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.224em; border-left: 0px solid; width: 0px; height: 2.935em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>z</mi><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>2</mn><mrow><mn>1</mn><mo>+</mo><msup><mrow class="MJX-TeXAtom-ORD"><mtext>i</mtext></mrow><mn>7</mn></msup></mrow></mfrac></mstyle></mrow></math></span></span><script type="math/tex" id="MathJax-Element-44">{z=\dfrac{2}{1+\i^7}}</script> je</td></tr>
<tr><td><label for="odp7a">a) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-45-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-362" style="width: 0.618em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.506em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1000.49em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-363"><span class="mn" id="MathJax-Span-364" style="font-family: MathJax_Main;">0</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 0.958em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-45">0</script></label></td></tr>
<tr><td><label for="odp7b">b) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-46-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mtext>i</mtext></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-365" style="width: 2.462em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.015em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1002em, 2.406em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-366"><span class="mn" id="MathJax-Span-367" style="font-family: MathJax_Main;">2</span><span class="mo" id="MathJax-Span-368" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="texatom" id="MathJax-Span-369" style="padding-left: 0.226em;"><span class="mrow" id="MathJax-Span-370"><span class="mtext" id="MathJax-Span-371" style="font-family: MathJax_Main;">i</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.133em; border-left: 0px solid; width: 0px; height: 1.026em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mtext>i</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-46">2+\i</script></label></td></tr>
<tr><td><label for="odp7c">c) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-47-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-372" style="width: 0.618em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.506em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1000.43em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-373"><span class="mn" id="MathJax-Span-374" style="font-family: MathJax_Main;">1</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 0.958em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span></span><script type="math/tex" id="MathJax-Element-47">1</script></label></td></tr>
<tr><td><label for="odp7d">d) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-48-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>&#x2212;</mo><mrow class="MJX-TeXAtom-ORD"><mtext>i</mtext></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-375" style="width: 2.462em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.015em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1002em, 2.406em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-376"><span class="mn" id="MathJax-Span-377" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-378" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="texatom" id="MathJax-Span-379" style="padding-left: 0.226em;"><span class="mrow" id="MathJax-Span-380"><span class="mtext" id="MathJax-Span-381" style="font-family: MathJax_Main;">i</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.133em; border-left: 0px solid; width: 0px; height: 1.026em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mtext>i</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-48">1-\i</script></label></td></tr>
<tr><td><label for="odp7e">e) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-49-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mtext>i</mtext></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-382" style="width: 2.462em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.015em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1002em, 2.406em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-383"><span class="mn" id="MathJax-Span-384" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-385" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="texatom" id="MathJax-Span-386" style="padding-left: 0.226em;"><span class="mrow" id="MathJax-Span-387"><span class="mtext" id="MathJax-Span-388" style="font-family: MathJax_Main;">i</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.133em; border-left: 0px solid; width: 0px; height: 1.026em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mtext>i</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-49">1+\i</script></label></td></tr>
</tbody></table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tbody><tr>
<td class="licha jednoducha"><input name="8" id="odp8a" type="radio" value="1"><label for="odp8a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="8" id="odp8b" type="radio" value="2"><label for="odp8b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="8" id="odp8c" type="radio" value="3"><label for="odp8c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="8" id="odp8d" type="radio" value="4"><label for="odp8d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="8" id="odp8e" type="radio" value="5"><label for="odp8e">e</label></td>
</tr>
</tbody></table>
1 bod
</td>
<td>
<table class="otazky">
<tbody><tr><td>8. Výraz <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-50-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><msup><mrow><mo>(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><msup><mi>a</mi><mn>2</mn></msup><mrow><mi>a</mi><mo>+</mo><mn>2</mn></mrow></mfrac></mstyle><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mspace width="negativethinmathspace" /><mspace width="negativethinmathspace" /><mrow class="MJX-TeXAtom-ORD"><mo>&#x2212;</mo><mn>1</mn></mrow></mrow></msup><mspace width="negativethinmathspace" /><mo>&#x22C5;</mo><msup><mrow><mo>(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>&#x2212;</mo><mn>4</mn></mrow><mi>a</mi></mfrac></mstyle><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mspace width="negativethinmathspace" /><mspace width="negativethinmathspace" /><mrow class="MJX-TeXAtom-ORD"><mo>&#x2212;</mo><mn>1</mn></mrow></mrow></msup></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-389" style="width: 12.745em; display: inline-block;"><span style="display: inline-block; position: relative; width: 10.454em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.282em, 1010.43em, 3.3em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-390"><span class="texatom" id="MathJax-Span-391"><span class="mrow" id="MathJax-Span-392"><span class="msubsup" id="MathJax-Span-393"><span style="display: inline-block; position: relative; width: 4.753em; height: 0px;"><span style="position: absolute; clip: rect(2.35em, 1003.9em, 5.144em, -999.979em); top: -4.021em; left: 0em;"><span class="mrow" id="MathJax-Span-394"><span class="mo" id="MathJax-Span-395" style="vertical-align: 0em;"><span style="font-family: MathJax_Size3;">(</span></span><span class="mstyle" id="MathJax-Span-396"><span class="mrow" id="MathJax-Span-397"><span class="mfrac" id="MathJax-Span-398"><span style="display: inline-block; position: relative; width: 2.406em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.021em, 1000.93em, 4.194em, -999.979em); top: -4.692em; left: 50%; margin-left: -0.5em;"><span class="msubsup" id="MathJax-Span-399"><span style="display: inline-block; position: relative; width: 0.953em; height: 0px;"><span style="position: absolute; clip: rect(3.412em, 1000.49em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-400" style="font-family: MathJax_Math-italic;">a</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.356em; left: 0.506em;"><span class="mn" id="MathJax-Span-401" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.188em, 1002.22em, 4.25em, -999.979em); top: -3.35em; left: 50%; margin-left: -1.115em;"><span class="mrow" id="MathJax-Span-402"><span class="mi" id="MathJax-Span-403" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-404" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mn" id="MathJax-Span-405" style="font-family: MathJax_Main; padding-left: 0.226em;">2</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1002.39em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 2.406em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-406" style="vertical-align: 0em;"><span style="font-family: MathJax_Size3;">)</span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -5.251em; left: 4.083em;"><span class="texatom" id="MathJax-Span-407"><span class="mrow" id="MathJax-Span-408"><span class="mspace" id="MathJax-Span-409" style="height: 0em; vertical-align: 0em; margin-left: -0.165em;"><span style="display: inline-block; overflow: hidden; height: 1px; width: 0em;"></span></span><span class="mspace" id="MathJax-Span-410" style="height: 0em; vertical-align: 0em; margin-left: -0.165em;"></span><span class="texatom" id="MathJax-Span-411"><span class="mrow" id="MathJax-Span-412"><span class="mo" id="MathJax-Span-413" style="font-size: 70.7%; font-family: MathJax_Main;">−</span><span class="mn" id="MathJax-Span-414" style="font-size: 70.7%; font-family: MathJax_Main;">1</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mspace" id="MathJax-Span-415" style="height: 0em; vertical-align: 0em; margin-left: -0.165em;"></span><span class="mo" id="MathJax-Span-416" style="font-family: MathJax_Main; padding-left: 0.226em;">⋅</span><span class="msubsup" id="MathJax-Span-417" style="padding-left: 0.226em;"><span style="display: inline-block; position: relative; width: 5.144em; height: 0px;"><span style="position: absolute; clip: rect(2.35em, 1004.29em, 5.144em, -999.979em); top: -4.021em; left: 0em;"><span class="mrow" id="MathJax-Span-418"><span class="mo" id="MathJax-Span-419" style="vertical-align: 0em;"><span style="font-family: MathJax_Size3;">(</span></span><span class="mstyle" id="MathJax-Span-420"><span class="mrow" id="MathJax-Span-421"><span class="mfrac" id="MathJax-Span-422"><span style="display: inline-block; position: relative; width: 2.797em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.021em, 1002.67em, 4.25em, -999.979em); top: -4.692em; left: 50%; margin-left: -1.338em;"><span class="mrow" id="MathJax-Span-423"><span class="msubsup" id="MathJax-Span-424"><span style="display: inline-block; position: relative; width: 0.953em; height: 0px;"><span style="position: absolute; clip: rect(3.412em, 1000.49em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-425" style="font-family: MathJax_Math-italic;">a</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.356em; left: 0.506em;"><span class="mn" id="MathJax-Span-426" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-427" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-428" style="font-family: MathJax_Main; padding-left: 0.226em;">4</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.49em, 4.194em, -999.979em); top: -3.35em; left: 50%; margin-left: -0.277em;"><span class="mi" id="MathJax-Span-429" style="font-family: MathJax_Math-italic;">a</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1002.83em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 2.797em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-430" style="vertical-align: 0em;"><span style="font-family: MathJax_Size3;">)</span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -5.251em; left: 4.53em;"><span class="texatom" id="MathJax-Span-431"><span class="mrow" id="MathJax-Span-432"><span class="mspace" id="MathJax-Span-433" style="height: 0em; vertical-align: 0em; margin-left: -0.165em;"><span style="display: inline-block; overflow: hidden; height: 1px; width: 0em;"></span></span><span class="mspace" id="MathJax-Span-434" style="height: 0em; vertical-align: 0em; margin-left: -0.165em;"></span><span class="texatom" id="MathJax-Span-435"><span class="mrow" id="MathJax-Span-436"><span class="mo" id="MathJax-Span-437" style="font-size: 70.7%; font-family: MathJax_Main;">−</span><span class="mn" id="MathJax-Span-438" style="font-size: 70.7%; font-family: MathJax_Main;">1</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.224em; border-left: 0px solid; width: 0px; height: 3.413em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><msup><mrow><mo>(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><msup><mi>a</mi><mn>2</mn></msup><mrow><mi>a</mi><mo>+</mo><mn>2</mn></mrow></mfrac></mstyle><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mspace width="negativethinmathspace"></mspace><mspace width="negativethinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></mrow></msup><mspace width="negativethinmathspace"></mspace><mo>⋅</mo><msup><mrow><mo>(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn></mrow><mi>a</mi></mfrac></mstyle><mo>)</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mspace width="negativethinmathspace"></mspace><mspace width="negativethinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></mrow></msup></mrow></math></span></span><script type="math/tex" id="MathJax-Element-50">{\left(\dfrac{a^2}{a+2}\right)^{\!\!{-1}}\!\cdot \left(\dfrac{a^2-4}{a}\right)^{\!\!{-1}}}</script> je roven</td></tr>
<tr><td><label for="odp8a">a) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-51-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mi>a</mi><mo>&#x2212;</mo><mn>2</mn></mrow></mfrac></mstyle></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-439" style="width: 3.244em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.629em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.673em, 1002.61em, 3.132em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-440"><span class="texatom" id="MathJax-Span-441"><span class="mrow" id="MathJax-Span-442"><span class="mstyle" id="MathJax-Span-443"><span class="mrow" id="MathJax-Span-444"><span class="mfrac" id="MathJax-Span-445"><span style="display: inline-block; position: relative; width: 2.406em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.188em, 1000.43em, 4.194em, -999.979em); top: -4.692em; left: 50%; margin-left: -0.221em;"><span class="mn" id="MathJax-Span-446" style="font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.188em, 1002.22em, 4.25em, -999.979em); top: -3.35em; left: 50%; margin-left: -1.115em;"><span class="mrow" id="MathJax-Span-447"><span class="mi" id="MathJax-Span-448" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-449" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-450" style="font-family: MathJax_Main; padding-left: 0.226em;">2</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1002.39em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 2.406em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.019em; border-left: 0px solid; width: 0px; height: 2.731em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mi>a</mi><mo>−</mo><mn>2</mn></mrow></mfrac></mstyle></mrow></math></span></span><script type="math/tex" id="MathJax-Element-51">{\dfrac{1}{a-2}}</script>, pokud <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-52-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>a</mi><mo>&#x2260;</mo><mn>0</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace" /><mo>&#x2227;</mo><mspace width="thinmathspace" /></mrow><mi>a</mi><mo>&#x2260;</mo><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace" /><mo>&#x2227;</mo><mspace width="thinmathspace" /></mrow><mi>a</mi><mo>&#x2260;</mo><mo>&#x2212;</mo><mn>2</mn></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-451" style="width: 12.074em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.895em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1009.82em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-452"><span class="texatom" id="MathJax-Span-453"><span class="mrow" id="MathJax-Span-454"><span class="mi" id="MathJax-Span-455" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-456" style="font-family: MathJax_Main; padding-left: 0.282em;">≠</span><span class="mn" id="MathJax-Span-457" style="font-family: MathJax_Main; padding-left: 0.282em;">0</span><span class="texatom" id="MathJax-Span-458"><span class="mrow" id="MathJax-Span-459"><span class="mspace" id="MathJax-Span-460" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-461" style="font-family: MathJax_Main;">∧</span><span class="mspace" id="MathJax-Span-462" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span></span></span><span class="mi" id="MathJax-Span-463" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-464" style="font-family: MathJax_Main; padding-left: 0.282em;">≠</span><span class="mn" id="MathJax-Span-465" style="font-family: MathJax_Main; padding-left: 0.282em;">2</span><span class="texatom" id="MathJax-Span-466"><span class="mrow" id="MathJax-Span-467"><span class="mspace" id="MathJax-Span-468" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-469" style="font-family: MathJax_Main;">∧</span><span class="mspace" id="MathJax-Span-470" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span></span></span><span class="mi" id="MathJax-Span-471" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-472" style="font-family: MathJax_Main; padding-left: 0.282em;">≠</span><span class="mo" id="MathJax-Span-473" style="font-family: MathJax_Main; padding-left: 0.282em;">−</span><span class="mn" id="MathJax-Span-474" style="font-family: MathJax_Main;">2</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.299em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>a</mi><mo>≠</mo><mn>0</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace"></mspace><mo>∧</mo><mspace width="thinmathspace"></mspace></mrow><mi>a</mi><mo>≠</mo><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace"></mspace><mo>∧</mo><mspace width="thinmathspace"></mspace></mrow><mi>a</mi><mo>≠</mo><mo>−</mo><mn>2</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-52">{a\ne0\lland a\ne2\lland a\ne-2}</script></label></td></tr>
<tr><td><label for="odp8b">b) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-53-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mi>a</mi><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mfrac></mstyle></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-475" style="width: 4.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.915em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.673em, 1003.9em, 3.356em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-476"><span class="texatom" id="MathJax-Span-477"><span class="mrow" id="MathJax-Span-478"><span class="mstyle" id="MathJax-Span-479"><span class="mrow" id="MathJax-Span-480"><span class="mfrac" id="MathJax-Span-481"><span style="display: inline-block; position: relative; width: 3.691em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.188em, 1000.43em, 4.194em, -999.979em); top: -4.692em; left: 50%; margin-left: -0.221em;"><span class="mn" id="MathJax-Span-482" style="font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.132em, 1003.45em, 4.418em, -999.979em); top: -3.295em; left: 50%; margin-left: -1.786em;"><span class="mrow" id="MathJax-Span-483"><span class="mi" id="MathJax-Span-484" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-485" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-486" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-487" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mn" id="MathJax-Span-488" style="font-family: MathJax_Main; padding-left: 0.226em;">2</span><span class="mo" id="MathJax-Span-489" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1003.67em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 3.691em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.292em; border-left: 0px solid; width: 0px; height: 3.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mi>a</mi><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mfrac></mstyle></mrow></math></span></span><script type="math/tex" id="MathJax-Element-53">{\dfrac{1}{a(a+2)}}</script>, pokud <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-54-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>a</mi><mo>&#x2260;</mo><mn>0</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace" /><mo>&#x2227;</mo><mspace width="thinmathspace" /></mrow><mi>a</mi><mo>&#x2260;</mo><mo>&#x2212;</mo><mn>2</mn></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-490" style="width: 7.995em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.542em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1006.47em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-491"><span class="texatom" id="MathJax-Span-492"><span class="mrow" id="MathJax-Span-493"><span class="mi" id="MathJax-Span-494" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-495" style="font-family: MathJax_Main; padding-left: 0.282em;">≠</span><span class="mn" id="MathJax-Span-496" style="font-family: MathJax_Main; padding-left: 0.282em;">0</span><span class="texatom" id="MathJax-Span-497"><span class="mrow" id="MathJax-Span-498"><span class="mspace" id="MathJax-Span-499" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-500" style="font-family: MathJax_Main;">∧</span><span class="mspace" id="MathJax-Span-501" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span></span></span><span class="mi" id="MathJax-Span-502" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-503" style="font-family: MathJax_Main; padding-left: 0.282em;">≠</span><span class="mo" id="MathJax-Span-504" style="font-family: MathJax_Main; padding-left: 0.282em;">−</span><span class="mn" id="MathJax-Span-505" style="font-family: MathJax_Main;">2</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.299em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>a</mi><mo>≠</mo><mn>0</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace"></mspace><mo>∧</mo><mspace width="thinmathspace"></mspace></mrow><mi>a</mi><mo>≠</mo><mo>−</mo><mn>2</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-54">{a\ne0\lland a\ne-2}</script></label></td></tr>
<tr><td><label for="odp8c">c) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-55-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mi>a</mi><mo stretchy="false">(</mo><mi>a</mi><mo>&#x2212;</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mfrac></mstyle></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-506" style="width: 4.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.915em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.673em, 1003.9em, 3.356em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-507"><span class="texatom" id="MathJax-Span-508"><span class="mrow" id="MathJax-Span-509"><span class="mstyle" id="MathJax-Span-510"><span class="mrow" id="MathJax-Span-511"><span class="mfrac" id="MathJax-Span-512"><span style="display: inline-block; position: relative; width: 3.691em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.188em, 1000.43em, 4.194em, -999.979em); top: -4.692em; left: 50%; margin-left: -0.221em;"><span class="mn" id="MathJax-Span-513" style="font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.132em, 1003.45em, 4.418em, -999.979em); top: -3.295em; left: 50%; margin-left: -1.786em;"><span class="mrow" id="MathJax-Span-514"><span class="mi" id="MathJax-Span-515" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-516" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-517" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-518" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-519" style="font-family: MathJax_Main; padding-left: 0.226em;">2</span><span class="mo" id="MathJax-Span-520" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1003.67em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 3.691em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.292em; border-left: 0px solid; width: 0px; height: 3.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mi>a</mi><mo stretchy="false">(</mo><mi>a</mi><mo>−</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mfrac></mstyle></mrow></math></span></span><script type="math/tex" id="MathJax-Element-55">{\dfrac{1}{a(a-2)}}</script>, pokud <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-56-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>a</mi><mo>&#x2260;</mo><mn>0</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace" /><mo>&#x2227;</mo><mspace width="thinmathspace" /></mrow><mi>a</mi><mo>&#x2260;</mo><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace" /><mo>&#x2227;</mo><mspace width="thinmathspace" /></mrow><mi>a</mi><mo>&#x2260;</mo><mo>&#x2212;</mo><mn>2</mn></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-521" style="width: 12.074em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.895em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1009.82em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-522"><span class="texatom" id="MathJax-Span-523"><span class="mrow" id="MathJax-Span-524"><span class="mi" id="MathJax-Span-525" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-526" style="font-family: MathJax_Main; padding-left: 0.282em;">≠</span><span class="mn" id="MathJax-Span-527" style="font-family: MathJax_Main; padding-left: 0.282em;">0</span><span class="texatom" id="MathJax-Span-528"><span class="mrow" id="MathJax-Span-529"><span class="mspace" id="MathJax-Span-530" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-531" style="font-family: MathJax_Main;">∧</span><span class="mspace" id="MathJax-Span-532" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span></span></span><span class="mi" id="MathJax-Span-533" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-534" style="font-family: MathJax_Main; padding-left: 0.282em;">≠</span><span class="mn" id="MathJax-Span-535" style="font-family: MathJax_Main; padding-left: 0.282em;">2</span><span class="texatom" id="MathJax-Span-536"><span class="mrow" id="MathJax-Span-537"><span class="mspace" id="MathJax-Span-538" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-539" style="font-family: MathJax_Main;">∧</span><span class="mspace" id="MathJax-Span-540" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span></span></span><span class="mi" id="MathJax-Span-541" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-542" style="font-family: MathJax_Main; padding-left: 0.282em;">≠</span><span class="mo" id="MathJax-Span-543" style="font-family: MathJax_Main; padding-left: 0.282em;">−</span><span class="mn" id="MathJax-Span-544" style="font-family: MathJax_Main;">2</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.299em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>a</mi><mo>≠</mo><mn>0</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace"></mspace><mo>∧</mo><mspace width="thinmathspace"></mspace></mrow><mi>a</mi><mo>≠</mo><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace"></mspace><mo>∧</mo><mspace width="thinmathspace"></mspace></mrow><mi>a</mi><mo>≠</mo><mo>−</mo><mn>2</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-56">{a\ne0\lland a\ne2\lland a\ne-2}</script></label></td></tr>
<tr><td><label for="odp8d">d) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-57-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mi>a</mi><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mfrac></mstyle></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-545" style="width: 4.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.915em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.673em, 1003.9em, 3.356em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-546"><span class="texatom" id="MathJax-Span-547"><span class="mrow" id="MathJax-Span-548"><span class="mstyle" id="MathJax-Span-549"><span class="mrow" id="MathJax-Span-550"><span class="mfrac" id="MathJax-Span-551"><span style="display: inline-block; position: relative; width: 3.691em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.188em, 1000.43em, 4.194em, -999.979em); top: -4.692em; left: 50%; margin-left: -0.221em;"><span class="mn" id="MathJax-Span-552" style="font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.132em, 1003.45em, 4.418em, -999.979em); top: -3.295em; left: 50%; margin-left: -1.786em;"><span class="mrow" id="MathJax-Span-553"><span class="mi" id="MathJax-Span-554" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-555" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-556" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-557" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mn" id="MathJax-Span-558" style="font-family: MathJax_Main; padding-left: 0.226em;">2</span><span class="mo" id="MathJax-Span-559" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1003.67em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 3.691em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.292em; border-left: 0px solid; width: 0px; height: 3.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mi>a</mi><mo stretchy="false">(</mo><mi>a</mi><mo>+</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mfrac></mstyle></mrow></math></span></span><script type="math/tex" id="MathJax-Element-57">{\dfrac{1}{a(a+2)}}</script>, pokud <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-58-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>a</mi><mo>&#x2260;</mo><mn>0</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace" /><mo>&#x2227;</mo><mspace width="thinmathspace" /></mrow><mi>a</mi><mo>&#x2260;</mo><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace" /><mo>&#x2227;</mo><mspace width="thinmathspace" /></mrow><mi>a</mi><mo>&#x2260;</mo><mo>&#x2212;</mo><mn>2</mn></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-560" style="width: 12.074em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.895em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1009.82em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-561"><span class="texatom" id="MathJax-Span-562"><span class="mrow" id="MathJax-Span-563"><span class="mi" id="MathJax-Span-564" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-565" style="font-family: MathJax_Main; padding-left: 0.282em;">≠</span><span class="mn" id="MathJax-Span-566" style="font-family: MathJax_Main; padding-left: 0.282em;">0</span><span class="texatom" id="MathJax-Span-567"><span class="mrow" id="MathJax-Span-568"><span class="mspace" id="MathJax-Span-569" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-570" style="font-family: MathJax_Main;">∧</span><span class="mspace" id="MathJax-Span-571" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span></span></span><span class="mi" id="MathJax-Span-572" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-573" style="font-family: MathJax_Main; padding-left: 0.282em;">≠</span><span class="mn" id="MathJax-Span-574" style="font-family: MathJax_Main; padding-left: 0.282em;">2</span><span class="texatom" id="MathJax-Span-575"><span class="mrow" id="MathJax-Span-576"><span class="mspace" id="MathJax-Span-577" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-578" style="font-family: MathJax_Main;">∧</span><span class="mspace" id="MathJax-Span-579" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span></span></span><span class="mi" id="MathJax-Span-580" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-581" style="font-family: MathJax_Main; padding-left: 0.282em;">≠</span><span class="mo" id="MathJax-Span-582" style="font-family: MathJax_Main; padding-left: 0.282em;">−</span><span class="mn" id="MathJax-Span-583" style="font-family: MathJax_Main;">2</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.299em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>a</mi><mo>≠</mo><mn>0</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace"></mspace><mo>∧</mo><mspace width="thinmathspace"></mspace></mrow><mi>a</mi><mo>≠</mo><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace"></mspace><mo>∧</mo><mspace width="thinmathspace"></mspace></mrow><mi>a</mi><mo>≠</mo><mo>−</mo><mn>2</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-58">{a\ne0\lland a\ne2\lland a\ne-2}</script></label></td></tr>
<tr><td><label for="odp8e">e) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-59-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mi>a</mi><mo stretchy="false">(</mo><mi>a</mi><mo>&#x2212;</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mfrac></mstyle></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-584" style="width: 4.809em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.915em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.673em, 1003.9em, 3.356em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-585"><span class="texatom" id="MathJax-Span-586"><span class="mrow" id="MathJax-Span-587"><span class="mstyle" id="MathJax-Span-588"><span class="mrow" id="MathJax-Span-589"><span class="mfrac" id="MathJax-Span-590"><span style="display: inline-block; position: relative; width: 3.691em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.188em, 1000.43em, 4.194em, -999.979em); top: -4.692em; left: 50%; margin-left: -0.221em;"><span class="mn" id="MathJax-Span-591" style="font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.132em, 1003.45em, 4.418em, -999.979em); top: -3.295em; left: 50%; margin-left: -1.786em;"><span class="mrow" id="MathJax-Span-592"><span class="mi" id="MathJax-Span-593" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-594" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-595" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-596" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-597" style="font-family: MathJax_Main; padding-left: 0.226em;">2</span><span class="mo" id="MathJax-Span-598" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1003.67em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 3.691em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.292em; border-left: 0px solid; width: 0px; height: 3.003em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mi>a</mi><mo stretchy="false">(</mo><mi>a</mi><mo>−</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></mfrac></mstyle></mrow></math></span></span><script type="math/tex" id="MathJax-Element-59">{\dfrac{1}{a(a-2)}}</script>, pokud <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-60-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>a</mi><mo>&#x2260;</mo><mn>0</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace" /><mo>&#x2227;</mo><mspace width="thinmathspace" /></mrow><mi>a</mi><mo>&#x2260;</mo><mn>2</mn></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-599" style="width: 7.045em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1005.68em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-600"><span class="texatom" id="MathJax-Span-601"><span class="mrow" id="MathJax-Span-602"><span class="mi" id="MathJax-Span-603" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-604" style="font-family: MathJax_Main; padding-left: 0.282em;">≠</span><span class="mn" id="MathJax-Span-605" style="font-family: MathJax_Main; padding-left: 0.282em;">0</span><span class="texatom" id="MathJax-Span-606"><span class="mrow" id="MathJax-Span-607"><span class="mspace" id="MathJax-Span-608" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-609" style="font-family: MathJax_Main;">∧</span><span class="mspace" id="MathJax-Span-610" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span></span></span><span class="mi" id="MathJax-Span-611" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-612" style="font-family: MathJax_Main; padding-left: 0.282em;">≠</span><span class="mn" id="MathJax-Span-613" style="font-family: MathJax_Main; padding-left: 0.282em;">2</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.299em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>a</mi><mo>≠</mo><mn>0</mn><mrow class="MJX-TeXAtom-ORD"><mspace width="thinmathspace"></mspace><mo>∧</mo><mspace width="thinmathspace"></mspace></mrow><mi>a</mi><mo>≠</mo><mn>2</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-60">{a\ne0\lland a\ne2}</script></label></td></tr>
</tbody></table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tbody><tr>
<td class="licha jednoducha"><input name="9" id="odp9a" type="radio" value="1"><label for="odp9a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="9" id="odp9b" type="radio" value="2"><label for="odp9b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="9" id="odp9c" type="radio" value="3"><label for="odp9c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="9" id="odp9d" type="radio" value="4"><label for="odp9d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="9" id="odp9e" type="radio" value="5"><label for="odp9e">e</label></td>
</tr>
</tbody></table>
1 bod
</td>
<td>
<table class="otazky">
<tbody><tr><td>9. Množinou všech řešení rovnice <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-61-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><msup><mi>sin</mi><mn>2</mn></msup><mo>&#x2061;</mo><mi>x</mi><mo>+</mo><mi>cos</mi><mo>&#x2061;</mo><mi>x</mi><mo>&#x2212;</mo><mn>1</mn><mo>=</mo><mn>0</mn></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-614" style="width: 11.348em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.28em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.121em, 1009.26em, 2.406em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-615"><span class="texatom" id="MathJax-Span-616"><span class="mrow" id="MathJax-Span-617"><span class="msubsup" id="MathJax-Span-618"><span style="display: inline-block; position: relative; width: 1.679em; height: 0px;"><span style="position: absolute; clip: rect(3.188em, 1001.21em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-619" style="font-family: MathJax_Main;">sin</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.412em; left: 1.232em;"><span class="mn" id="MathJax-Span-620" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-621"></span><span class="mi" id="MathJax-Span-622" style="font-family: MathJax_Math-italic; padding-left: 0.17em;">x</span><span class="mo" id="MathJax-Span-623" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mi" id="MathJax-Span-624" style="font-family: MathJax_Main; padding-left: 0.226em;">cos</span><span class="mo" id="MathJax-Span-625"></span><span class="mi" id="MathJax-Span-626" style="font-family: MathJax_Math-italic; padding-left: 0.17em;">x</span><span class="mo" id="MathJax-Span-627" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-628" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span><span class="mo" id="MathJax-Span-629" style="font-family: MathJax_Main; padding-left: 0.282em;">=</span><span class="mn" id="MathJax-Span-630" style="font-family: MathJax_Main; padding-left: 0.282em;">0</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.133em; border-left: 0px solid; width: 0px; height: 1.299em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><msup><mi>sin</mi><mn>2</mn></msup><mo></mo><mi>x</mi><mo>+</mo><mi>cos</mi><mo></mo><mi>x</mi><mo>−</mo><mn>1</mn><mo>=</mo><mn>0</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-61">{\sin^2x+\cos x-1=0}</script> je</td></tr>
<tr><td><label for="odp9a">a) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-62-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>&#x22C3;</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>&#x2208;</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>&#x03C0;</mi><mo>+</mo><mn>2</mn><mi>k</mi><mi>&#x03C0;</mi><mo>,</mo><mspace width="thinmathspace" /><mi>k</mi><mi>&#x03C0;</mi><mo fence="false" stretchy="false">}</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-631" style="width: 11.012em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.001em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.121em, 1008.93em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-632"><span class="munderover" id="MathJax-Span-633"><span style="display: inline-block; position: relative; width: 2.238em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.77em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-634" style="font-family: MathJax_Size1; vertical-align: 0em;">⋃</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -3.742em; left: 0.841em;"><span class="texatom" id="MathJax-Span-635"><span class="mrow" id="MathJax-Span-636"><span class="mi" id="MathJax-Span-637" style="font-size: 70.7%; font-family: MathJax_Math-italic;">k</span><span class="mo" id="MathJax-Span-638" style="font-size: 70.7%; font-family: MathJax_Main;">∈</span><span class="texatom" id="MathJax-Span-639"><span class="mrow" id="MathJax-Span-640"><span class="texatom" id="MathJax-Span-641"><span class="mrow" id="MathJax-Span-642"><span class="mi" id="MathJax-Span-643" style="font-size: 70.7%; font-family: MathJax_AMS;">Z</span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-644" style="font-family: MathJax_Main;">{</span><span class="mfrac" id="MathJax-Span-645"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.412em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-646" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-647" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mi" id="MathJax-Span-648" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-649" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mn" id="MathJax-Span-650" style="font-family: MathJax_Main; padding-left: 0.226em;">2</span><span class="mi" id="MathJax-Span-651" style="font-family: MathJax_Math-italic;">k</span><span class="mi" id="MathJax-Span-652" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-653" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-654" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-655" style="font-family: MathJax_Math-italic; padding-left: 0.17em;">k</span><span class="mi" id="MathJax-Span-656" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-657" style="font-family: MathJax_Main;">}</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>∈</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>π</mi><mo>+</mo><mn>2</mn><mi>k</mi><mi>π</mi><mo>,</mo><mspace width="thinmathspace"></mspace><mi>k</mi><mi>π</mi><mo fence="false" stretchy="false">}</mo></math></span></span><script type="math/tex" id="MathJax-Element-62">\bigcup_{k\in\Z} \{\frac12\pi+2k\pi,\,k\pi\}</script></label></td></tr>
<tr><td><label for="odp9b">b) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-63-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>&#x22C3;</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>&#x2208;</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mn>2</mn><mi>k</mi><mi>&#x03C0;</mi><mo fence="false" stretchy="false">}</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-658" style="width: 5.871em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.809em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1004.74em, 2.685em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-659"><span class="munderover" id="MathJax-Span-660"><span style="display: inline-block; position: relative; width: 2.238em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.77em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-661" style="font-family: MathJax_Size1; vertical-align: 0em;">⋃</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -3.742em; left: 0.841em;"><span class="texatom" id="MathJax-Span-662"><span class="mrow" id="MathJax-Span-663"><span class="mi" id="MathJax-Span-664" style="font-size: 70.7%; font-family: MathJax_Math-italic;">k</span><span class="mo" id="MathJax-Span-665" style="font-size: 70.7%; font-family: MathJax_Main;">∈</span><span class="texatom" id="MathJax-Span-666"><span class="mrow" id="MathJax-Span-667"><span class="texatom" id="MathJax-Span-668"><span class="mrow" id="MathJax-Span-669"><span class="mi" id="MathJax-Span-670" style="font-size: 70.7%; font-family: MathJax_AMS;">Z</span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-671" style="font-family: MathJax_Main;">{</span><span class="mn" id="MathJax-Span-672" style="font-family: MathJax_Main;">2</span><span class="mi" id="MathJax-Span-673" style="font-family: MathJax_Math-italic;">k</span><span class="mi" id="MathJax-Span-674" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-675" style="font-family: MathJax_Main;">}</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.474em; border-left: 0px solid; width: 0px; height: 1.435em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>∈</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mn>2</mn><mi>k</mi><mi>π</mi><mo fence="false" stretchy="false">}</mo></math></span></span><script type="math/tex" id="MathJax-Element-63">\bigcup_{k\in\Z} \{2k\pi\}</script></label></td></tr>
<tr><td><label for="odp9c">c) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-64-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>&#x22C3;</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>&#x2208;</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>&#x03C0;</mi><mo>+</mo><mi>k</mi><mi>&#x03C0;</mi><mo fence="false" stretchy="false">}</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-676" style="width: 8.33em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.821em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.121em, 1006.75em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-677"><span class="munderover" id="MathJax-Span-678"><span style="display: inline-block; position: relative; width: 2.238em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.77em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-679" style="font-family: MathJax_Size1; vertical-align: 0em;">⋃</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -3.742em; left: 0.841em;"><span class="texatom" id="MathJax-Span-680"><span class="mrow" id="MathJax-Span-681"><span class="mi" id="MathJax-Span-682" style="font-size: 70.7%; font-family: MathJax_Math-italic;">k</span><span class="mo" id="MathJax-Span-683" style="font-size: 70.7%; font-family: MathJax_Main;">∈</span><span class="texatom" id="MathJax-Span-684"><span class="mrow" id="MathJax-Span-685"><span class="texatom" id="MathJax-Span-686"><span class="mrow" id="MathJax-Span-687"><span class="mi" id="MathJax-Span-688" style="font-size: 70.7%; font-family: MathJax_AMS;">Z</span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-689" style="font-family: MathJax_Main;">{</span><span class="mfrac" id="MathJax-Span-690"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.412em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-691" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-692" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mi" id="MathJax-Span-693" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-694" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mi" id="MathJax-Span-695" style="font-family: MathJax_Math-italic; padding-left: 0.226em;">k</span><span class="mi" id="MathJax-Span-696" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-697" style="font-family: MathJax_Main;">}</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>∈</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>π</mi><mo>+</mo><mi>k</mi><mi>π</mi><mo fence="false" stretchy="false">}</mo></math></span></span><script type="math/tex" id="MathJax-Element-64">\bigcup_{k\in\Z} \{\frac12\pi+k\pi\}</script></label></td></tr>
<tr><td><label for="odp9d">d) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-65-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>&#x22C3;</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>&#x2208;</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>&#x03C0;</mi><mo>+</mo><mi>k</mi><mi>&#x03C0;</mi><mo>,</mo><mspace width="thinmathspace" /><mn>2</mn><mi>k</mi><mi>&#x03C0;</mi><mo fence="false" stretchy="false">}</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-698" style="width: 11.012em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.001em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.121em, 1008.93em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-699"><span class="munderover" id="MathJax-Span-700"><span style="display: inline-block; position: relative; width: 2.238em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.77em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-701" style="font-family: MathJax_Size1; vertical-align: 0em;">⋃</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -3.742em; left: 0.841em;"><span class="texatom" id="MathJax-Span-702"><span class="mrow" id="MathJax-Span-703"><span class="mi" id="MathJax-Span-704" style="font-size: 70.7%; font-family: MathJax_Math-italic;">k</span><span class="mo" id="MathJax-Span-705" style="font-size: 70.7%; font-family: MathJax_Main;">∈</span><span class="texatom" id="MathJax-Span-706"><span class="mrow" id="MathJax-Span-707"><span class="texatom" id="MathJax-Span-708"><span class="mrow" id="MathJax-Span-709"><span class="mi" id="MathJax-Span-710" style="font-size: 70.7%; font-family: MathJax_AMS;">Z</span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-711" style="font-family: MathJax_Main;">{</span><span class="mfrac" id="MathJax-Span-712"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.412em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-713" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-714" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mi" id="MathJax-Span-715" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-716" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mi" id="MathJax-Span-717" style="font-family: MathJax_Math-italic; padding-left: 0.226em;">k</span><span class="mi" id="MathJax-Span-718" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-719" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-720" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-721" style="font-family: MathJax_Main; padding-left: 0.17em;">2</span><span class="mi" id="MathJax-Span-722" style="font-family: MathJax_Math-italic;">k</span><span class="mi" id="MathJax-Span-723" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-724" style="font-family: MathJax_Main;">}</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>∈</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>π</mi><mo>+</mo><mi>k</mi><mi>π</mi><mo>,</mo><mspace width="thinmathspace"></mspace><mn>2</mn><mi>k</mi><mi>π</mi><mo fence="false" stretchy="false">}</mo></math></span></span><script type="math/tex" id="MathJax-Element-65">\bigcup_{k\in\Z} \{\frac12\pi+k\pi,\,2k\pi\}</script></label></td></tr>
<tr><td><label for="odp9e">e) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-66-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>&#x22C3;</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>&#x2208;</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mi>k</mi><mi>&#x03C0;</mi><mo fence="false" stretchy="false">}</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-725" style="width: 5.256em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.306em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1004.23em, 2.685em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-726"><span class="munderover" id="MathJax-Span-727"><span style="display: inline-block; position: relative; width: 2.238em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.77em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-728" style="font-family: MathJax_Size1; vertical-align: 0em;">⋃</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -3.742em; left: 0.841em;"><span class="texatom" id="MathJax-Span-729"><span class="mrow" id="MathJax-Span-730"><span class="mi" id="MathJax-Span-731" style="font-size: 70.7%; font-family: MathJax_Math-italic;">k</span><span class="mo" id="MathJax-Span-732" style="font-size: 70.7%; font-family: MathJax_Main;">∈</span><span class="texatom" id="MathJax-Span-733"><span class="mrow" id="MathJax-Span-734"><span class="texatom" id="MathJax-Span-735"><span class="mrow" id="MathJax-Span-736"><span class="mi" id="MathJax-Span-737" style="font-size: 70.7%; font-family: MathJax_AMS;">Z</span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-738" style="font-family: MathJax_Main;">{</span><span class="mi" id="MathJax-Span-739" style="font-family: MathJax_Math-italic;">k</span><span class="mi" id="MathJax-Span-740" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-741" style="font-family: MathJax_Main;">}</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.474em; border-left: 0px solid; width: 0px; height: 1.435em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>∈</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mi>k</mi><mi>π</mi><mo fence="false" stretchy="false">}</mo></math></span></span><script type="math/tex" id="MathJax-Element-66">\bigcup_{k\in\Z} \{k\pi\}</script></label></td></tr>
</tbody></table>
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<tr>
<td>
<table class="odpovedi">
<tbody><tr>
<td class="licha jednoducha"><input name="10" id="odp10a" type="radio" value="1"><label for="odp10a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="10" id="odp10b" type="radio" value="2"><label for="odp10b">b</label></td>
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<tr>
<td> </td>
<td class="licha jednoducha"><input name="10" id="odp10c" type="radio" value="3"><label for="odp10c">c</label></td>
<td> </td>
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<td class="licha jednoducha"><input name="10" id="odp10d" type="radio" value="4"><label for="odp10d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="10" id="odp10e" type="radio" value="5"><label for="odp10e">e</label></td>
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1 bod
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<table class="otazky">
<tbody><tr><td>10. Jestliže <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-67-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>log</mi><mo>&#x2061;</mo><mi>y</mi><mo>=</mo><mn>2</mn><mi>log</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mo>&#x2212;</mo><mn>2</mn><mi>log</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mi>x</mi><mo>&#x2212;</mo><mn>1</mn><mo stretchy="false">)</mo><mo>+</mo><mn>1</mn></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-742" style="width: 19.843em; display: inline-block;"><span style="display: inline-block; position: relative; width: 16.266em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1016.19em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-743"><span class="texatom" id="MathJax-Span-744"><span class="mrow" id="MathJax-Span-745"><span class="mi" id="MathJax-Span-746" style="font-family: MathJax_Main;">log</span><span class="mo" id="MathJax-Span-747"></span><span class="mi" id="MathJax-Span-748" style="font-family: MathJax_Math-italic; padding-left: 0.17em;">y<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-749" style="font-family: MathJax_Main; padding-left: 0.282em;">=</span><span class="mn" id="MathJax-Span-750" style="font-family: MathJax_Main; padding-left: 0.282em;">2</span><span class="mi" id="MathJax-Span-751" style="font-family: MathJax_Main; padding-left: 0.17em;">log</span><span class="mo" id="MathJax-Span-752"></span><span class="mo" id="MathJax-Span-753" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-754" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-755" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mn" id="MathJax-Span-756" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span><span class="mo" id="MathJax-Span-757" style="font-family: MathJax_Main;">)</span><span class="mo" id="MathJax-Span-758" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-759" style="font-family: MathJax_Main; padding-left: 0.226em;">2</span><span class="mi" id="MathJax-Span-760" style="font-family: MathJax_Main; padding-left: 0.17em;">log</span><span class="mo" id="MathJax-Span-761"></span><span class="mo" id="MathJax-Span-762" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-763" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-764" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-765" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span><span class="mo" id="MathJax-Span-766" style="font-family: MathJax_Main;">)</span><span class="mo" id="MathJax-Span-767" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mn" id="MathJax-Span-768" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>log</mi><mo></mo><mi>y</mi><mo>=</mo><mn>2</mn><mi>log</mi><mo></mo><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mo>−</mo><mn>2</mn><mi>log</mi><mo></mo><mo stretchy="false">(</mo><mi>x</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo>+</mo><mn>1</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-67">{\log y=2\log(x+1)-2\log(x-1)+1}</script>, pak číslo <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-68-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-769" style="width: 0.618em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.506em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.568em, 1000.49em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-770"><span class="mi" id="MathJax-Span-771" style="font-family: MathJax_Math-italic;">y<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 0.958em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></span></span><script type="math/tex" id="MathJax-Element-68">y</script> je rovno</td></tr>
<tr><td><label for="odp10a">a) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-69-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>&#x2212;</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow></mfrac></mstyle></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-772" style="width: 4.697em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.859em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.45em, 1003.84em, 3.356em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-773"><span class="mstyle" id="MathJax-Span-774"><span class="mrow" id="MathJax-Span-775"><span class="mfrac" id="MathJax-Span-776"><span style="display: inline-block; position: relative; width: 3.635em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.021em, 1003.5em, 4.418em, -999.979em); top: -4.748em; left: 50%; margin-left: -1.73em;"><span class="mrow" id="MathJax-Span-777"><span class="mo" id="MathJax-Span-778" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-779" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-780" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mn" id="MathJax-Span-781" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span><span class="msubsup" id="MathJax-Span-782"><span style="display: inline-block; position: relative; width: 0.841em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.32em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-783" style="font-family: MathJax_Main;">)</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.356em; left: 0.394em;"><span class="mn" id="MathJax-Span-784" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.077em, 1003.5em, 4.418em, -999.979em); top: -3.295em; left: 50%; margin-left: -1.73em;"><span class="mrow" id="MathJax-Span-785"><span class="mo" id="MathJax-Span-786" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-787" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-788" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-789" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span><span class="msubsup" id="MathJax-Span-790"><span style="display: inline-block; position: relative; width: 0.841em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.32em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-791" style="font-family: MathJax_Main;">)</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.3em; left: 0.394em;"><span class="mn" id="MathJax-Span-792" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1003.62em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 3.635em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.292em; border-left: 0px solid; width: 0px; height: 3.276em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow></mfrac></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-69">\dfrac{(x+1)^2}{(x-1)^2}</script></label></td></tr>
<tr><td><label for="odp10b">b) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-70-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>10</mn><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><mrow><mi>x</mi><mo>&#x2212;</mo><mn>1</mn></mrow></mfrac></mstyle></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-793" style="width: 5.424em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.418em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.562em, 1004.4em, 3.132em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-794"><span class="mstyle" id="MathJax-Span-795"><span class="mrow" id="MathJax-Span-796"><span class="mfrac" id="MathJax-Span-797"><span style="display: inline-block; position: relative; width: 4.194em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.132em, 1004.01em, 4.418em, -999.979em); top: -4.748em; left: 50%; margin-left: -2.065em;"><span class="mrow" id="MathJax-Span-798"><span class="mn" id="MathJax-Span-799" style="font-family: MathJax_Main;">10</span><span class="mo" id="MathJax-Span-800" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-801" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-802" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mn" id="MathJax-Span-803" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span><span class="mo" id="MathJax-Span-804" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.188em, 1002.22em, 4.25em, -999.979em); top: -3.35em; left: 50%; margin-left: -1.171em;"><span class="mrow" id="MathJax-Span-805"><span class="mi" id="MathJax-Span-806" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-807" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-808" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1004.18em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 4.194em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.019em; border-left: 0px solid; width: 0px; height: 2.867em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>10</mn><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-70">\dfrac{10(x+1)}{x-1}</script></label></td></tr>
<tr><td><label for="odp10c">c) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-71-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mpadded width="0"><mphantom><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle></mphantom></mpadded></mrow></mrow><mn>1</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-809" style="width: 0.618em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.506em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.673em, 1000.43em, 3.021em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-810"><span class="texatom" id="MathJax-Span-811"><span class="mrow" id="MathJax-Span-812"><span class="texatom" id="MathJax-Span-813"><span class="mrow" id="MathJax-Span-814"><span class="mpadded" id="MathJax-Span-815"><span style="display: inline-block; position: relative; width: 0em; height: 0px;"><span style="position: absolute; clip: rect(2.518em, 999.984em, 4.865em, -999.979em); top: -4.021em; left: 0em;"><span class="mrow" id="MathJax-Span-816"><span class="mphantom" id="MathJax-Span-817"><span class="mrow" id="MathJax-Span-818" style="visibility: hidden;"><span class="mstyle" id="MathJax-Span-819"><span class="mrow" id="MathJax-Span-820"><span class="mfrac" id="MathJax-Span-821"><span style="display: inline-block; position: relative; width: 0.618em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.188em, 1000.43em, 4.194em, -999.979em); top: -4.692em; left: 50%; margin-left: -0.221em;"><span class="mn" id="MathJax-Span-822" style="font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.188em, 1000.43em, 4.194em, -999.979em); top: -3.35em; left: 50%; margin-left: -0.221em;"><span class="mn" id="MathJax-Span-823" style="font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.6em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.618em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span></span></span></span><span class="mn" id="MathJax-Span-824" style="font-family: MathJax_Main;">1</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.883em; border-left: 0px solid; width: 0px; height: 2.594em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mpadded width="0"><mphantom><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle></mphantom></mpadded></mrow></mrow><mn>1</mn></math></span></span><script type="math/tex" id="MathJax-Element-71">\str 1</script></label></td></tr>
<tr><td><label for="odp10d">d) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-72-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>10</mn><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>&#x2212;</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow></mfrac></mstyle></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-825" style="width: 5.927em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.865em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.45em, 1004.85em, 3.356em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-826"><span class="mstyle" id="MathJax-Span-827"><span class="mrow" id="MathJax-Span-828"><span class="mfrac" id="MathJax-Span-829"><span style="display: inline-block; position: relative; width: 4.641em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.021em, 1004.51em, 4.418em, -999.979em); top: -4.748em; left: 50%; margin-left: -2.233em;"><span class="mrow" id="MathJax-Span-830"><span class="mn" id="MathJax-Span-831" style="font-family: MathJax_Main;">10</span><span class="mo" id="MathJax-Span-832" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-833" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-834" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mn" id="MathJax-Span-835" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span><span class="msubsup" id="MathJax-Span-836"><span style="display: inline-block; position: relative; width: 0.841em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.32em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-837" style="font-family: MathJax_Main;">)</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.356em; left: 0.394em;"><span class="mn" id="MathJax-Span-838" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.077em, 1003.5em, 4.418em, -999.979em); top: -3.295em; left: 50%; margin-left: -1.73em;"><span class="mrow" id="MathJax-Span-839"><span class="mo" id="MathJax-Span-840" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-841" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-842" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-843" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span><span class="msubsup" id="MathJax-Span-844"><span style="display: inline-block; position: relative; width: 0.841em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.32em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-845" style="font-family: MathJax_Main;">)</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.3em; left: 0.394em;"><span class="mn" id="MathJax-Span-846" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1004.62em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 4.641em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.292em; border-left: 0px solid; width: 0px; height: 3.276em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>10</mn><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow></mfrac></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-72">\dfrac{10(x+1)^2}{(x-1)^2}</script></label></td></tr>
<tr><td><label for="odp10e">e) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-73-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>&#x2212;</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><mrow><mn>10</mn><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow></mfrac></mstyle></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-847" style="width: 5.927em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.865em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.45em, 1004.85em, 3.356em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-848"><span class="mstyle" id="MathJax-Span-849"><span class="mrow" id="MathJax-Span-850"><span class="mfrac" id="MathJax-Span-851"><span style="display: inline-block; position: relative; width: 4.641em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.021em, 1003.5em, 4.418em, -999.979em); top: -4.748em; left: 50%; margin-left: -1.73em;"><span class="mrow" id="MathJax-Span-852"><span class="mo" id="MathJax-Span-853" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-854" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-855" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-856" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span><span class="msubsup" id="MathJax-Span-857"><span style="display: inline-block; position: relative; width: 0.841em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.32em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-858" style="font-family: MathJax_Main;">)</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.356em; left: 0.394em;"><span class="mn" id="MathJax-Span-859" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.077em, 1004.51em, 4.418em, -999.979em); top: -3.295em; left: 50%; margin-left: -2.233em;"><span class="mrow" id="MathJax-Span-860"><span class="mn" id="MathJax-Span-861" style="font-family: MathJax_Main;">10</span><span class="mo" id="MathJax-Span-862" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-863" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-864" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mn" id="MathJax-Span-865" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span><span class="msubsup" id="MathJax-Span-866"><span style="display: inline-block; position: relative; width: 0.841em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.32em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-867" style="font-family: MathJax_Main;">)</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.3em; left: 0.394em;"><span class="mn" id="MathJax-Span-868" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1004.62em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 4.641em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.292em; border-left: 0px solid; width: 0px; height: 3.276em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><mrow><mn>10</mn><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow></mfrac></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-73">\dfrac{(x-1)^2}{10(x+1)^2}</script></label></td></tr>
</tbody></table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tbody><tr>
<td class="licha jednoducha"><input name="11" id="odp11a" type="radio" value="1"><label for="odp11a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="11" id="odp11b" type="radio" value="2"><label for="odp11b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="11" id="odp11c" type="radio" value="3"><label for="odp11c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="11" id="odp11d" type="radio" value="4"><label for="odp11d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="11" id="odp11e" type="radio" value="5"><label for="odp11e">e</label></td>
</tr>
</tbody></table>
1 bod
</td>
<td>
<table class="otazky">
<tbody><tr><td>11. Graf funkce <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-74-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>y</mi><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mtr><mtd><mi>x</mi><mo>&#x2212;</mo><mn>3</mn></mtd><mtd><mstyle displaystyle="false" scriptlevel="0"><mtext>pro&#xA0;</mtext><mrow class="MJX-TeXAtom-ORD"><mi>x</mi><mo>&#x2264;</mo><mn>3</mn></mrow></mstyle><mo>,</mo></mtd></mtr><mtr><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mn>3</mn><mo>&#x2212;</mo><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mstyle displaystyle="false" scriptlevel="0"><mtext>pro&#xA0;</mtext><mrow class="MJX-TeXAtom-ORD"><mi>x</mi><mo>&gt;</mo><mn>3</mn></mrow></mstyle></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true"></mo></mrow></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-869" style="width: 13.639em; display: inline-block;"><span style="display: inline-block; position: relative; width: 11.18em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.791em, 1011.16em, 4.53em, -999.979em); top: -3.406em; left: 0em;"><span class="mrow" id="MathJax-Span-870"><span class="texatom" id="MathJax-Span-871"><span class="mrow" id="MathJax-Span-872"><span class="mi" id="MathJax-Span-873" style="font-family: MathJax_Math-italic;">y<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-874" style="font-family: MathJax_Main; padding-left: 0.282em;">=</span><span class="mrow" id="MathJax-Span-875" style="padding-left: 0.282em;"><span class="mo" id="MathJax-Span-876" style="vertical-align: 0em;"><span style="font-family: MathJax_Size3;">{</span></span><span class="mtable" id="MathJax-Span-877"><span style="display: inline-block; position: relative; width: 8.274em; height: 0px; margin-right: 0.17em; margin-left: 0.17em;"><span style="position: absolute; clip: rect(2.629em, 1002.72em, 5.088em, -999.979em); top: -4.021em; left: 0em;"><span style="display: inline-block; position: relative; width: 2.853em; height: 0px;"><span style="position: absolute; clip: rect(3.188em, 1002.28em, 4.25em, -999.979em); top: -4.58em; left: 0em;"><span class="mtd" id="MathJax-Span-878"><span class="mrow" id="MathJax-Span-879"><span class="mi" id="MathJax-Span-880" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-881" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-882" style="font-family: MathJax_Main; padding-left: 0.226em;">3</span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.132em, 1002.72em, 4.418em, -999.979em); top: -3.406em; left: 0em;"><span class="mtd" id="MathJax-Span-894"><span class="mrow" id="MathJax-Span-895"><span class="texatom" id="MathJax-Span-896"><span class="mrow" id="MathJax-Span-897"><span class="mo" id="MathJax-Span-898" style="font-family: MathJax_Main;">|</span></span></span><span class="mn" id="MathJax-Span-899" style="font-family: MathJax_Main;">3</span><span class="mo" id="MathJax-Span-900" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mi" id="MathJax-Span-901" style="font-family: MathJax_Math-italic; padding-left: 0.226em;">x</span><span class="texatom" id="MathJax-Span-902"><span class="mrow" id="MathJax-Span-903"><span class="mo" id="MathJax-Span-904" style="font-family: MathJax_Main;">|</span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(2.629em, 1004.34em, 5.033em, -999.979em); top: -4.021em; left: 3.859em;"><span style="display: inline-block; position: relative; width: 4.418em; height: 0px;"><span style="position: absolute; clip: rect(3.188em, 1004.34em, 4.362em, -999.979em); top: -4.58em; left: 0em;"><span class="mtd" id="MathJax-Span-883"><span class="mrow" id="MathJax-Span-884"><span class="mstyle" id="MathJax-Span-885"><span class="mrow" id="MathJax-Span-886"><span class="mtext" id="MathJax-Span-887" style="font-family: MathJax_Main;">pro </span><span class="texatom" id="MathJax-Span-888"><span class="mrow" id="MathJax-Span-889"><span class="mi" id="MathJax-Span-890" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-891" style="font-family: MathJax_Main; padding-left: 0.282em;">≤</span><span class="mn" id="MathJax-Span-892" style="font-family: MathJax_Main; padding-left: 0.282em;">3</span></span></span></span></span><span class="mo" id="MathJax-Span-893" style="font-family: MathJax_Main;">,</span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.188em, 1004.06em, 4.362em, -999.979em); top: -3.406em; left: 0em;"><span class="mtd" id="MathJax-Span-905"><span class="mrow" id="MathJax-Span-906"><span class="mstyle" id="MathJax-Span-907"><span class="mrow" id="MathJax-Span-908"><span class="mtext" id="MathJax-Span-909" style="font-family: MathJax_Main;">pro </span><span class="texatom" id="MathJax-Span-910"><span class="mrow" id="MathJax-Span-911"><span class="mi" id="MathJax-Span-912" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-913" style="font-family: MathJax_Main; padding-left: 0.282em;">></span><span class="mn" id="MathJax-Span-914" style="font-family: MathJax_Main; padding-left: 0.282em;">3</span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-915"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.412em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.224em; border-left: 0px solid; width: 0px; height: 3.072em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>y</mi><mo>=</mo><mrow><mo>{</mo><mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mtr><mtd><mi>x</mi><mo>−</mo><mn>3</mn></mtd><mtd><mstyle displaystyle="false" scriptlevel="0"><mtext>pro </mtext><mrow class="MJX-TeXAtom-ORD"><mi>x</mi><mo>≤</mo><mn>3</mn></mrow></mstyle><mo>,</mo></mtd></mtr><mtr><mtd><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mn>3</mn><mo>−</mo><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mtd><mtd><mstyle displaystyle="false" scriptlevel="0"><mtext>pro </mtext><mrow class="MJX-TeXAtom-ORD"><mi>x</mi><mo>></mo><mn>3</mn></mrow></mstyle></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true"></mo></mrow></mrow></math></span></span><script type="math/tex" id="MathJax-Element-74">{y=\begin{cases} x-3&\hbox{pro $x\le3$},\\ |3-x|&\hbox{pro $x>3$}\end{cases}}</script></td></tr>
<tr><td><label for="odp11a">a) je polopřímka</label></td></tr>
<tr><td><label for="odp11b">b) je úsečka</label></td></tr>
<tr><td><label for="odp11c">c) jsou dvě různoběžné polopřímky bez společného bodu</label></td></tr>
<tr><td><label for="odp11d">d) je přímka</label></td></tr>
<tr><td><label for="odp11e">e) jsou dvě různoběžné polopřímky se společným počátečním bodem</label></td></tr>
</tbody></table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tbody><tr>
<td class="licha jednoducha"><input name="12" id="odp12a" type="radio" value="1"><label for="odp12a">a</label></td>
<td> </td>
<td class="licha jednoducha"><input name="12" id="odp12b" type="radio" value="2"><label for="odp12b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha jednoducha"><input name="12" id="odp12c" type="radio" value="3"><label for="odp12c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha jednoducha"><input name="12" id="odp12d" type="radio" value="4"><label for="odp12d">d</label></td>
<td> </td>
<td class="licha jednoducha"><input name="12" id="odp12e" type="radio" value="5"><label for="odp12e">e</label></td>
</tr>
</tbody></table>
1 bod
</td>
<td>
<table class="otazky">
<tbody><tr><td>12. Maximální definiční obor funkce <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-75-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>&#x2212;</mo><msup><mi>sin</mi><mn>2</mn></msup><mo>&#x2061;</mo><mi>x</mi><mo stretchy="false">)</mo><mo>&#x22C5;</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-OP"><mtext>tg</mtext><mspace width="thinmathspace" /></mrow></mrow><mi>x</mi></mrow><mrow><msup><mi>cos</mi><mn>2</mn></msup><mo>&#x2061;</mo><mi>x</mi><mo>&#x2212;</mo><mn>1</mn></mrow></mfrac></mstyle></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-916" style="width: 13.248em; display: inline-block;"><span style="display: inline-block; position: relative; width: 10.845em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.394em, 1010.83em, 3.188em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-917"><span class="texatom" id="MathJax-Span-918"><span class="mrow" id="MathJax-Span-919"><span class="mi" id="MathJax-Span-920" style="font-family: MathJax_Math-italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.059em;"></span></span><span class="mo" id="MathJax-Span-921" style="font-family: MathJax_Main;">(</span><span class="mi" id="MathJax-Span-922" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-923" style="font-family: MathJax_Main;">)</span><span class="mo" id="MathJax-Span-924" style="font-family: MathJax_Main; padding-left: 0.282em;">=</span><span class="mstyle" id="MathJax-Span-925" style="padding-left: 0.282em;"><span class="mrow" id="MathJax-Span-926"><span class="mfrac" id="MathJax-Span-927"><span style="display: inline-block; position: relative; width: 7.38em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(2.965em, 1007.19em, 4.418em, -999.979em); top: -4.748em; left: 50%; margin-left: -3.63em;"><span class="mrow" id="MathJax-Span-928"><span class="mo" id="MathJax-Span-929" style="font-family: MathJax_Main;">(</span><span class="mn" id="MathJax-Span-930" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-931" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="msubsup" id="MathJax-Span-932" style="padding-left: 0.226em;"><span style="display: inline-block; position: relative; width: 1.679em; height: 0px;"><span style="position: absolute; clip: rect(3.188em, 1001.21em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-933" style="font-family: MathJax_Main;">sin</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.412em; left: 1.232em;"><span class="mn" id="MathJax-Span-934" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-935"></span><span class="mi" id="MathJax-Span-936" style="font-family: MathJax_Math-italic; padding-left: 0.17em;">x</span><span class="mo" id="MathJax-Span-937" style="font-family: MathJax_Main;">)</span><span class="mo" id="MathJax-Span-938" style="font-family: MathJax_Main; padding-left: 0.226em;">⋅</span><span class="texatom" id="MathJax-Span-939" style="padding-left: 0.226em;"><span class="mrow" id="MathJax-Span-940"><span class="texatom" id="MathJax-Span-941"><span class="mrow" id="MathJax-Span-942"><span class="mtext" id="MathJax-Span-943" style="font-family: MathJax_Main;">tg</span><span class="mspace" id="MathJax-Span-944" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span></span></span></span></span><span class="mi" id="MathJax-Span-945" style="font-family: MathJax_Math-italic;">x</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.077em, 1004.18em, 4.25em, -999.979em); top: -3.295em; left: 50%; margin-left: -2.121em;"><span class="mrow" id="MathJax-Span-946"><span class="msubsup" id="MathJax-Span-947"><span style="display: inline-block; position: relative; width: 1.791em; height: 0px;"><span style="position: absolute; clip: rect(3.412em, 1001.33em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-948" style="font-family: MathJax_Main;">cos</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.3em; left: 1.344em;"><span class="mn" id="MathJax-Span-949" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-950"></span><span class="mi" id="MathJax-Span-951" style="font-family: MathJax_Math-italic; padding-left: 0.17em;">x</span><span class="mo" id="MathJax-Span-952" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-953" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1007.36em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 7.38em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.088em; border-left: 0px solid; width: 0px; height: 3.072em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msup><mi>sin</mi><mn>2</mn></msup><mo></mo><mi>x</mi><mo stretchy="false">)</mo><mo>⋅</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-OP"><mtext>tg</mtext><mspace width="thinmathspace"></mspace></mrow></mrow><mi>x</mi></mrow><mrow><msup><mi>cos</mi><mn>2</mn></msup><mo></mo><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mstyle></mrow></math></span></span><script type="math/tex" id="MathJax-Element-75">{f(x)=\dfrac{(1-\sin^2x)\cdot\tg x}{\cos^2 x-1}}</script> je</td></tr>
<tr><td><label for="odp12a">a) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-76-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">R</mi></mrow></mrow><mo>&#x2212;</mo><munder><mo>&#x22C3;</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>&#x2208;</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>&#x03C0;</mi><mo>+</mo><mi>k</mi><mi>&#x03C0;</mi><mo fence="false" stretchy="false">}</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-954" style="width: 10.733em; display: inline-block;"><span style="display: inline-block; position: relative; width: 8.777em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.4em, 1008.7em, 3.021em, -999.979em); top: -2.456em; left: 0em;"><span class="mrow" id="MathJax-Span-955"><span class="texatom" id="MathJax-Span-956"><span class="mrow" id="MathJax-Span-957"><span class="texatom" id="MathJax-Span-958"><span class="mrow" id="MathJax-Span-959"><span class="mi" id="MathJax-Span-960" style="font-family: MathJax_AMS;">R</span></span></span></span></span><span class="mo" id="MathJax-Span-961" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="munderover" id="MathJax-Span-962" style="padding-left: 0.226em;"><span style="display: inline-block; position: relative; width: 2.238em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.77em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-963" style="font-family: MathJax_Size1; vertical-align: 0em;">⋃</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -3.742em; left: 0.841em;"><span class="texatom" id="MathJax-Span-964"><span class="mrow" id="MathJax-Span-965"><span class="mi" id="MathJax-Span-966" style="font-size: 70.7%; font-family: MathJax_Math-italic;">k</span><span class="mo" id="MathJax-Span-967" style="font-size: 70.7%; font-family: MathJax_Main;">∈</span><span class="texatom" id="MathJax-Span-968"><span class="mrow" id="MathJax-Span-969"><span class="texatom" id="MathJax-Span-970"><span class="mrow" id="MathJax-Span-971"><span class="mi" id="MathJax-Span-972" style="font-size: 70.7%; font-family: MathJax_AMS;">Z</span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-973" style="font-family: MathJax_Main;">{</span><span class="mfrac" id="MathJax-Span-974"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.412em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-975" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-976" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mi" id="MathJax-Span-977" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-978" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mi" id="MathJax-Span-979" style="font-family: MathJax_Math-italic; padding-left: 0.226em;">k</span><span class="mi" id="MathJax-Span-980" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-981" style="font-family: MathJax_Main;">}</span></span><span style="display: inline-block; width: 0px; height: 2.462em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">R</mi></mrow></mrow><mo>−</mo><munder><mo>⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>∈</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>π</mi><mo>+</mo><mi>k</mi><mi>π</mi><mo fence="false" stretchy="false">}</mo></math></span></span><script type="math/tex" id="MathJax-Element-76">\R-\bigcup_{k\in\Z} \{\frac12\pi+k\pi\}</script></label></td></tr>
<tr><td><label for="odp12b">b) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-77-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">R</mi></mrow></mrow><mo>&#x2212;</mo><munder><mo>&#x22C3;</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>&#x2208;</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>&#x03C0;</mi><mo>+</mo><mn>2</mn><mi>k</mi><mi>&#x03C0;</mi><mo fence="false" stretchy="false">}</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-982" style="width: 11.348em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.28em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.4em, 1009.21em, 3.021em, -999.979em); top: -2.456em; left: 0em;"><span class="mrow" id="MathJax-Span-983"><span class="texatom" id="MathJax-Span-984"><span class="mrow" id="MathJax-Span-985"><span class="texatom" id="MathJax-Span-986"><span class="mrow" id="MathJax-Span-987"><span class="mi" id="MathJax-Span-988" style="font-family: MathJax_AMS;">R</span></span></span></span></span><span class="mo" id="MathJax-Span-989" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="munderover" id="MathJax-Span-990" style="padding-left: 0.226em;"><span style="display: inline-block; position: relative; width: 2.238em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.77em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-991" style="font-family: MathJax_Size1; vertical-align: 0em;">⋃</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -3.742em; left: 0.841em;"><span class="texatom" id="MathJax-Span-992"><span class="mrow" id="MathJax-Span-993"><span class="mi" id="MathJax-Span-994" style="font-size: 70.7%; font-family: MathJax_Math-italic;">k</span><span class="mo" id="MathJax-Span-995" style="font-size: 70.7%; font-family: MathJax_Main;">∈</span><span class="texatom" id="MathJax-Span-996"><span class="mrow" id="MathJax-Span-997"><span class="texatom" id="MathJax-Span-998"><span class="mrow" id="MathJax-Span-999"><span class="mi" id="MathJax-Span-1000" style="font-size: 70.7%; font-family: MathJax_AMS;">Z</span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-1001" style="font-family: MathJax_Main;">{</span><span class="mfrac" id="MathJax-Span-1002"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.412em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-1003" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-1004" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mi" id="MathJax-Span-1005" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-1006" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mn" id="MathJax-Span-1007" style="font-family: MathJax_Main; padding-left: 0.226em;">2</span><span class="mi" id="MathJax-Span-1008" style="font-family: MathJax_Math-italic;">k</span><span class="mi" id="MathJax-Span-1009" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-1010" style="font-family: MathJax_Main;">}</span></span><span style="display: inline-block; width: 0px; height: 2.462em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">R</mi></mrow></mrow><mo>−</mo><munder><mo>⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>∈</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>π</mi><mo>+</mo><mn>2</mn><mi>k</mi><mi>π</mi><mo fence="false" stretchy="false">}</mo></math></span></span><script type="math/tex" id="MathJax-Element-77">\R-\bigcup_{k\in\Z} \{\frac12\pi+2k\pi\}</script></label></td></tr>
<tr><td><label for="odp12c">c) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-78-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>&#x22C3;</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>&#x2208;</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo stretchy="false">(</mo><mn>2</mn><mi>k</mi><mi>&#x03C0;</mi><mo>,</mo><mspace width="thinmathspace" /><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>&#x03C0;</mi><mo>+</mo><mn>2</mn><mi>k</mi><mi>&#x03C0;</mi><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1011" style="width: 11.348em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.28em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.121em, 1009.21em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1012"><span class="munderover" id="MathJax-Span-1013"><span style="display: inline-block; position: relative; width: 2.238em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.77em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-1014" style="font-family: MathJax_Size1; vertical-align: 0em;">⋃</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -3.742em; left: 0.841em;"><span class="texatom" id="MathJax-Span-1015"><span class="mrow" id="MathJax-Span-1016"><span class="mi" id="MathJax-Span-1017" style="font-size: 70.7%; font-family: MathJax_Math-italic;">k</span><span class="mo" id="MathJax-Span-1018" style="font-size: 70.7%; font-family: MathJax_Main;">∈</span><span class="texatom" id="MathJax-Span-1019"><span class="mrow" id="MathJax-Span-1020"><span class="texatom" id="MathJax-Span-1021"><span class="mrow" id="MathJax-Span-1022"><span class="mi" id="MathJax-Span-1023" style="font-size: 70.7%; font-family: MathJax_AMS;">Z</span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-1024" style="font-family: MathJax_Main;">(</span><span class="mn" id="MathJax-Span-1025" style="font-family: MathJax_Main;">2</span><span class="mi" id="MathJax-Span-1026" style="font-family: MathJax_Math-italic;">k</span><span class="mi" id="MathJax-Span-1027" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-1028" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-1029" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mfrac" id="MathJax-Span-1030" style="padding-left: 0.17em;"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.412em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-1031" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-1032" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mi" id="MathJax-Span-1033" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-1034" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mn" id="MathJax-Span-1035" style="font-family: MathJax_Main; padding-left: 0.226em;">2</span><span class="mi" id="MathJax-Span-1036" style="font-family: MathJax_Math-italic;">k</span><span class="mi" id="MathJax-Span-1037" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-1038" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>∈</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo stretchy="false">(</mo><mn>2</mn><mi>k</mi><mi>π</mi><mo>,</mo><mspace width="thinmathspace"></mspace><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>π</mi><mo>+</mo><mn>2</mn><mi>k</mi><mi>π</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-78">\bigcup_{k\in\Z} (2k\pi,\,\frac12\pi+2k\pi)</script></label></td></tr>
<tr><td><label for="odp12d">d) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-79-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>&#x22C3;</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>&#x2208;</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo stretchy="false">(</mo><mn>2</mn><mi>k</mi><mi>&#x03C0;</mi><mo>,</mo><mspace width="thinmathspace" /><mo stretchy="false">(</mo><mn>2</mn><mi>k</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi>&#x03C0;</mi><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1039" style="width: 11.404em; display: inline-block;"><span style="display: inline-block; position: relative; width: 9.336em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1009.26em, 2.685em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1040"><span class="munderover" id="MathJax-Span-1041"><span style="display: inline-block; position: relative; width: 2.238em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.77em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-1042" style="font-family: MathJax_Size1; vertical-align: 0em;">⋃</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -3.742em; left: 0.841em;"><span class="texatom" id="MathJax-Span-1043"><span class="mrow" id="MathJax-Span-1044"><span class="mi" id="MathJax-Span-1045" style="font-size: 70.7%; font-family: MathJax_Math-italic;">k</span><span class="mo" id="MathJax-Span-1046" style="font-size: 70.7%; font-family: MathJax_Main;">∈</span><span class="texatom" id="MathJax-Span-1047"><span class="mrow" id="MathJax-Span-1048"><span class="texatom" id="MathJax-Span-1049"><span class="mrow" id="MathJax-Span-1050"><span class="mi" id="MathJax-Span-1051" style="font-size: 70.7%; font-family: MathJax_AMS;">Z</span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-1052" style="font-family: MathJax_Main;">(</span><span class="mn" id="MathJax-Span-1053" style="font-family: MathJax_Main;">2</span><span class="mi" id="MathJax-Span-1054" style="font-family: MathJax_Math-italic;">k</span><span class="mi" id="MathJax-Span-1055" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-1056" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-1057" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-1058" style="font-family: MathJax_Main; padding-left: 0.17em;">(</span><span class="mn" id="MathJax-Span-1059" style="font-family: MathJax_Main;">2</span><span class="mi" id="MathJax-Span-1060" style="font-family: MathJax_Math-italic;">k</span><span class="mo" id="MathJax-Span-1061" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mn" id="MathJax-Span-1062" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span><span class="mo" id="MathJax-Span-1063" style="font-family: MathJax_Main;">)</span><span class="mi" id="MathJax-Span-1064" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-1065" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.474em; border-left: 0px solid; width: 0px; height: 1.435em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>∈</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo stretchy="false">(</mo><mn>2</mn><mi>k</mi><mi>π</mi><mo>,</mo><mspace width="thinmathspace"></mspace><mo stretchy="false">(</mo><mn>2</mn><mi>k</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi>π</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-79">\bigcup_{k\in\Z} (2k\pi,\,(2k+1)\pi)</script></label></td></tr>
<tr><td><label for="odp12e">e) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-80-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">R</mi></mrow></mrow><mo>&#x2212;</mo><munder><mo>&#x22C3;</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>&#x2208;</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>k</mi><mi>&#x03C0;</mi><mo fence="false" stretchy="false">}</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1066" style="width: 8.553em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.989em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.4em, 1006.91em, 3.021em, -999.979em); top: -2.456em; left: 0em;"><span class="mrow" id="MathJax-Span-1067"><span class="texatom" id="MathJax-Span-1068"><span class="mrow" id="MathJax-Span-1069"><span class="texatom" id="MathJax-Span-1070"><span class="mrow" id="MathJax-Span-1071"><span class="mi" id="MathJax-Span-1072" style="font-family: MathJax_AMS;">R</span></span></span></span></span><span class="mo" id="MathJax-Span-1073" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="munderover" id="MathJax-Span-1074" style="padding-left: 0.226em;"><span style="display: inline-block; position: relative; width: 2.238em; height: 0px;"><span style="position: absolute; clip: rect(3.132em, 1000.77em, 4.418em, -999.979em); top: -4.021em; left: 0em;"><span class="mo" id="MathJax-Span-1075" style="font-family: MathJax_Size1; vertical-align: 0em;">⋃</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -3.742em; left: 0.841em;"><span class="texatom" id="MathJax-Span-1076"><span class="mrow" id="MathJax-Span-1077"><span class="mi" id="MathJax-Span-1078" style="font-size: 70.7%; font-family: MathJax_Math-italic;">k</span><span class="mo" id="MathJax-Span-1079" style="font-size: 70.7%; font-family: MathJax_Main;">∈</span><span class="texatom" id="MathJax-Span-1080"><span class="mrow" id="MathJax-Span-1081"><span class="texatom" id="MathJax-Span-1082"><span class="mrow" id="MathJax-Span-1083"><span class="mi" id="MathJax-Span-1084" style="font-size: 70.7%; font-family: MathJax_AMS;">Z</span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-1085" style="font-family: MathJax_Main;">{</span><span class="mfrac" id="MathJax-Span-1086"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.412em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-1087" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-1088" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mi" id="MathJax-Span-1089" style="font-family: MathJax_Math-italic;">k</span><span class="mi" id="MathJax-Span-1090" style="font-family: MathJax_Math-italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-1091" style="font-family: MathJax_Main;">}</span></span><span style="display: inline-block; width: 0px; height: 2.462em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">R</mi></mrow></mrow><mo>−</mo><munder><mo>⋃</mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>∈</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">Z</mi></mrow></mrow></mrow></munder><mo fence="false" stretchy="false">{</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>k</mi><mi>π</mi><mo fence="false" stretchy="false">}</mo></math></span></span><script type="math/tex" id="MathJax-Element-80">\R-\bigcup_{k\in\Z} \{\frac12k\pi\}</script></label></td></tr>
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<tbody><tr><td>13. Množinou všech řešení nerovnice <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-81-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mrow><mo>|</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>&#x2212;</mo><mn>1</mn></mrow></mfrac></mstyle><mo>|</mo></mrow><mo>&gt;</mo><mn>3</mn></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1092" style="width: 6.15em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.033em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(2.015em, 1005.01em, 4.53em, -999.979em); top: -3.518em; left: 0em;"><span class="mrow" id="MathJax-Span-1093"><span class="texatom" id="MathJax-Span-1094"><span class="mrow" id="MathJax-Span-1095"><span class="mrow" id="MathJax-Span-1096"><span class="mo" id="MathJax-Span-1097" style="vertical-align: 1.344em;"><span style="display: inline-block; position: relative; width: 0.282em; height: 0px;"><span style="position: absolute; font-family: MathJax_Main; top: -3.295em; left: 0em;">∣<span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; font-family: MathJax_Main; top: -2.065em; left: 0em;">∣<span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="font-family: MathJax_Main; position: absolute; top: -2.68em; left: 0em;">∣<span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mstyle" id="MathJax-Span-1098"><span class="mrow" id="MathJax-Span-1099"><span class="mfrac" id="MathJax-Span-1100"><span style="display: inline-block; position: relative; width: 2.406em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.188em, 1002.22em, 4.25em, -999.979em); top: -4.692em; left: 50%; margin-left: -1.171em;"><span class="mrow" id="MathJax-Span-1101"><span class="mi" id="MathJax-Span-1102" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-1103" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mn" id="MathJax-Span-1104" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.188em, 1002.22em, 4.25em, -999.979em); top: -3.35em; left: 50%; margin-left: -1.171em;"><span class="mrow" id="MathJax-Span-1105"><span class="mi" id="MathJax-Span-1106" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-1107" style="font-family: MathJax_Main; padding-left: 0.226em;">−</span><span class="mn" id="MathJax-Span-1108" style="font-family: MathJax_Main; padding-left: 0.226em;">1</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1002.44em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 2.406em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-1109" style="vertical-align: 1.344em;"><span style="display: inline-block; position: relative; width: 0.282em; height: 0px;"><span style="position: absolute; font-family: MathJax_Main; top: -3.295em; left: 0em;">∣<span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; font-family: MathJax_Main; top: -2.065em; left: 0em;">∣<span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="font-family: MathJax_Main; position: absolute; top: -2.68em; left: 0em;">∣<span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span></span><span class="mo" id="MathJax-Span-1110" style="font-family: MathJax_Main; padding-left: 0.282em;">></span><span class="mn" id="MathJax-Span-1111" style="font-family: MathJax_Main; padding-left: 0.282em;">3</span></span></span></span><span style="display: inline-block; width: 0px; height: 3.524em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.088em; border-left: 0px solid; width: 0px; height: 2.799em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mrow><mo>|</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mstyle><mo>|</mo></mrow><mo>></mo><mn>3</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-81">{\left|\dfrac{x+1}{x-1}\right|>3}</script> s neznámou <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-82-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>x</mi><mo>&#x2208;</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">R</mi></mrow></mrow></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1112" style="width: 3.077em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.518em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.624em, 1002.5em, 2.685em, -999.979em); top: -2.456em; left: 0em;"><span class="mrow" id="MathJax-Span-1113"><span class="texatom" id="MathJax-Span-1114"><span class="mrow" id="MathJax-Span-1115"><span class="mi" id="MathJax-Span-1116" style="font-family: MathJax_Math-italic;">x</span><span class="mo" id="MathJax-Span-1117" style="font-family: MathJax_Main; padding-left: 0.282em;">∈</span><span class="texatom" id="MathJax-Span-1118" style="padding-left: 0.282em;"><span class="mrow" id="MathJax-Span-1119"><span class="texatom" id="MathJax-Span-1120"><span class="mrow" id="MathJax-Span-1121"><span class="mi" id="MathJax-Span-1122" style="font-family: MathJax_AMS;">R</span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.462em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.133em; border-left: 0px solid; width: 0px; height: 1.026em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>x</mi><mo>∈</mo><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">R</mi></mrow></mrow></mrow></math></span></span><script type="math/tex" id="MathJax-Element-82">{x\in\R}</script> je</td></tr>
<tr><td><label for="odp13a">a) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-83-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace" /><mi mathvariant="normal">&#x221E;</mi><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1123" style="width: 3.58em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.909em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1002.83em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1124"><span class="mo" id="MathJax-Span-1125" style="font-family: MathJax_Main;">(</span><span class="mn" id="MathJax-Span-1126" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-1127" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-1128" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-1129" style="font-family: MathJax_Main; padding-left: 0.17em;">∞</span><span class="mo" id="MathJax-Span-1130" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace"></mspace><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-83">(1,\,\infty)</script></label></td></tr>
<tr><td><label for="odp13b">b) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-84-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mo>&#x2212;</mo><mi mathvariant="normal">&#x221E;</mi><mo>,</mo><mspace width="thinmathspace" /><mo>&#x2212;</mo><mn>1</mn><mo stretchy="false">)</mo><mo>&#x222A;</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace" /><mi mathvariant="normal">&#x221E;</mi><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1131" style="width: 10.342em; display: inline-block;"><span style="display: inline-block; position: relative; width: 8.442em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1008.37em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1132"><span class="mo" id="MathJax-Span-1133" style="font-family: MathJax_Main;">(</span><span class="mo" id="MathJax-Span-1134" style="font-family: MathJax_Main;">−</span><span class="mi" id="MathJax-Span-1135" style="font-family: MathJax_Main;">∞</span><span class="mo" id="MathJax-Span-1136" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-1137" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mo" id="MathJax-Span-1138" style="font-family: MathJax_Main; padding-left: 0.17em;">−</span><span class="mn" id="MathJax-Span-1139" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-1140" style="font-family: MathJax_Main;">)</span><span class="mo" id="MathJax-Span-1141" style="font-family: MathJax_Main; padding-left: 0.226em;">∪</span><span class="mo" id="MathJax-Span-1142" style="font-family: MathJax_Main; padding-left: 0.226em;">(</span><span class="mn" id="MathJax-Span-1143" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-1144" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-1145" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mi" id="MathJax-Span-1146" style="font-family: MathJax_Main; padding-left: 0.17em;">∞</span><span class="mo" id="MathJax-Span-1147" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mo>−</mo><mi mathvariant="normal">∞</mi><mo>,</mo><mspace width="thinmathspace"></mspace><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo>∪</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace"></mspace><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-84">(-\infty,\,-1)\cup(1,\,\infty)</script></label></td></tr>
<tr><td><label for="odp13c">c) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-85-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mo>&#x2212;</mo><mi mathvariant="normal">&#x221E;</mi><mo>,</mo><mspace width="thinmathspace" /><mn>1</mn><mo stretchy="false">)</mo><mo>&#x222A;</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace" /><mn>2</mn><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1148" style="width: 8.833em; display: inline-block;"><span style="display: inline-block; position: relative; width: 7.212em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1007.14em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1149"><span class="mo" id="MathJax-Span-1150" style="font-family: MathJax_Main;">(</span><span class="mo" id="MathJax-Span-1151" style="font-family: MathJax_Main;">−</span><span class="mi" id="MathJax-Span-1152" style="font-family: MathJax_Main;">∞</span><span class="mo" id="MathJax-Span-1153" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-1154" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-1155" style="font-family: MathJax_Main; padding-left: 0.17em;">1</span><span class="mo" id="MathJax-Span-1156" style="font-family: MathJax_Main;">)</span><span class="mo" id="MathJax-Span-1157" style="font-family: MathJax_Main; padding-left: 0.226em;">∪</span><span class="mo" id="MathJax-Span-1158" style="font-family: MathJax_Main; padding-left: 0.226em;">(</span><span class="mn" id="MathJax-Span-1159" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-1160" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-1161" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-1162" style="font-family: MathJax_Main; padding-left: 0.17em;">2</span><span class="mo" id="MathJax-Span-1163" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mo>−</mo><mi mathvariant="normal">∞</mi><mo>,</mo><mspace width="thinmathspace"></mspace><mn>1</mn><mo stretchy="false">)</mo><mo>∪</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace"></mspace><mn>2</mn><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-85">(-\infty,\,1)\cup(1,\,2)</script></label></td></tr>
<tr><td><label for="odp13d">d) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-86-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-OPEN"><mo maxsize="1.2em" minsize="1.2em">(</mo></mrow></mstyle><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mspace width="thinmathspace" /><mn>1</mn><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-CLOSE"><mo maxsize="1.2em" minsize="1.2em">)</mo></mrow></mstyle><mo>&#x222A;</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace" /><mn>2</mn><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1164" style="width: 7.603em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.206em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.176em, 1006.13em, 2.797em, -999.979em); top: -2.233em; left: 0em;"><span class="mrow" id="MathJax-Span-1165"><span class="mstyle" id="MathJax-Span-1166" style=""><span class="mrow" id="MathJax-Span-1167"><span class="texatom" id="MathJax-Span-1168" style=""><span class="mrow" id="MathJax-Span-1169"><span class="mo" id="MathJax-Span-1170" style="vertical-align: 0em;"><span style="font-family: MathJax_Size1;">(</span></span></span></span></span></span><span class="mfrac" id="MathJax-Span-1171"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.412em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-1172" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-1173" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mo" id="MathJax-Span-1174" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-1175" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-1176" style="font-family: MathJax_Main; padding-left: 0.17em;">1</span><span class="mstyle" id="MathJax-Span-1177" style=""><span class="mrow" id="MathJax-Span-1178"><span class="texatom" id="MathJax-Span-1179" style=""><span class="mrow" id="MathJax-Span-1180"><span class="mo" id="MathJax-Span-1181" style="vertical-align: 0em;"><span style="font-family: MathJax_Size1;">)</span></span></span></span></span></span><span class="mo" id="MathJax-Span-1182" style="font-family: MathJax_Main; padding-left: 0.226em;">∪</span><span class="mo" id="MathJax-Span-1183" style="font-family: MathJax_Main; padding-left: 0.226em;">(</span><span class="mn" id="MathJax-Span-1184" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-1185" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-1186" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-1187" style="font-family: MathJax_Main; padding-left: 0.17em;">2</span><span class="mo" id="MathJax-Span-1188" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 2.238em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-OPEN"><mo maxsize="1.2em" minsize="1.2em">(</mo></mrow></mstyle><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mspace width="thinmathspace"></mspace><mn>1</mn><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-CLOSE"><mo maxsize="1.2em" minsize="1.2em">)</mo></mrow></mstyle><mo>∪</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace"></mspace><mn>2</mn><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-86">\bigl(\frac12,\,1\bigr)\cup(1,\,2)</script></label></td></tr>
<tr><td><label for="odp13e">e) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-87-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mo>&#x2212;</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace" /><mn>1</mn><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1189" style="width: 3.915em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.188em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1003.11em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1190"><span class="mo" id="MathJax-Span-1191" style="font-family: MathJax_Main;">(</span><span class="mo" id="MathJax-Span-1192" style="font-family: MathJax_Main;">−</span><span class="mn" id="MathJax-Span-1193" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-1194" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-1195" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-1196" style="font-family: MathJax_Main; padding-left: 0.17em;">1</span><span class="mo" id="MathJax-Span-1197" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace"></mspace><mn>1</mn><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-87">(-1,\,1)</script></label></td></tr>
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<table class="odpovedi">
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<td class="licha dvojita"><input name="14" id="odp14a" type="radio" value="1"><label for="odp14a">a</label></td>
<td> </td>
<td class="licha dvojita"><input name="14" id="odp14b" type="radio" value="2"><label for="odp14b">b</label></td>
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<td> </td>
<td class="licha dvojita"><input name="14" id="odp14c" type="radio" value="3"><label for="odp14c">c</label></td>
<td> </td>
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<td class="licha dvojita"><input name="14" id="odp14d" type="radio" value="4"><label for="odp14d">d</label></td>
<td> </td>
<td class="licha dvojita"><input name="14" id="odp14e" type="radio" value="5"><label for="odp14e">e</label></td>
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2 body
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<table class="otazky">
<tbody><tr><td>14. Poměr obsahů pravidelného šestiúhelníku a do něho vepsaného kruhu je</td></tr>
<tr><td><label for="odp14a">a) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-88-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt><mo>:</mo><mi>&#x03C0;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1198" style="width: 3.356em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.741em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.176em, 1002.72em, 2.518em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1199"><span class="msqrt" id="MathJax-Span-1200"><span style="display: inline-block; position: relative; width: 1.344em; height: 0px;"><span style="position: absolute; clip: rect(3.188em, 1000.43em, 4.194em, -999.979em); top: -4.021em; left: 0.841em;"><span class="mrow" id="MathJax-Span-1201"><span class="mn" id="MathJax-Span-1202" style="font-family: MathJax_Main;">2</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.58em, 1000.49em, 3.971em, -999.979em); top: -4.58em; left: 0.841em;"><span style="font-family: MathJax_Main;">–</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.077em, 1000.88em, 4.418em, -999.979em); top: -4.077em; left: 0em;"><span style="font-family: MathJax_Main;">√</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-1203" style="font-family: MathJax_Main; padding-left: 0.282em;">:</span><span class="mi" id="MathJax-Span-1204" style="font-family: MathJax_Math-italic; padding-left: 0.282em;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.269em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt><mo>:</mo><mi>π</mi></math></span></span><script type="math/tex" id="MathJax-Element-88">\sqrt2:\pi</script></label></td></tr>
<tr><td><label for="odp14b">b) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-89-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:</mo><mi>&#x03C0;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1205" style="width: 2.406em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.959em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.568em, 1001.94em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1206"><span class="mi" id="MathJax-Span-1207" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-1208" style="font-family: MathJax_Main; padding-left: 0.282em;">:</span><span class="mi" id="MathJax-Span-1209" style="font-family: MathJax_Math-italic; padding-left: 0.282em;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 0.685em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>:</mo><mi>π</mi></math></span></span><script type="math/tex" id="MathJax-Element-89">a:\pi</script></label></td></tr>
<tr><td><label for="odp14c">c) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-90-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>a</mi><mn>2</mn></msup><mo>:</mo><mi>&#x03C0;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1210" style="width: 2.909em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.35em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.176em, 1002.33em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1211"><span class="msubsup" id="MathJax-Span-1212"><span style="display: inline-block; position: relative; width: 0.953em; height: 0px;"><span style="position: absolute; clip: rect(3.412em, 1000.49em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-1213" style="font-family: MathJax_Math-italic;">a</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.356em; left: 0.506em;"><span class="mn" id="MathJax-Span-1214" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-1215" style="font-family: MathJax_Main; padding-left: 0.282em;">:</span><span class="mi" id="MathJax-Span-1216" style="font-family: MathJax_Math-italic; padding-left: 0.282em;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 1.163em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>a</mi><mn>2</mn></msup><mo>:</mo><mi>π</mi></math></span></span><script type="math/tex" id="MathJax-Element-90">a^2:\pi</script></label></td></tr>
<tr><td><label for="odp14d">d) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-91-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>:</mo><mi>&#x03C0;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1217" style="width: 3.971em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.244em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.176em, 1003.23em, 2.518em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1218"><span class="mn" id="MathJax-Span-1219" style="font-family: MathJax_Main;">2</span><span class="msqrt" id="MathJax-Span-1220"><span style="display: inline-block; position: relative; width: 1.344em; height: 0px;"><span style="position: absolute; clip: rect(3.188em, 1000.49em, 4.194em, -999.979em); top: -4.021em; left: 0.841em;"><span class="mrow" id="MathJax-Span-1221"><span class="mn" id="MathJax-Span-1222" style="font-family: MathJax_Main;">3</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.58em, 1000.49em, 3.971em, -999.979em); top: -4.524em; left: 0.841em;"><span style="font-family: MathJax_Main;">–</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.077em, 1000.88em, 4.418em, -999.979em); top: -4.077em; left: 0em;"><span style="font-family: MathJax_Main;">√</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-1223" style="font-family: MathJax_Main; padding-left: 0.282em;">:</span><span class="mi" id="MathJax-Span-1224" style="font-family: MathJax_Math-italic; padding-left: 0.282em;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.269em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>:</mo><mi>π</mi></math></span></span><script type="math/tex" id="MathJax-Element-91">2\sqrt3:\pi</script></label></td></tr>
<tr><td><label for="odp14e">e) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-92-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn></msqrt><mo>:</mo><mi>&#x03C0;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1225" style="width: 3.356em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.741em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.176em, 1002.72em, 2.518em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1226"><span class="msqrt" id="MathJax-Span-1227"><span style="display: inline-block; position: relative; width: 1.344em; height: 0px;"><span style="position: absolute; clip: rect(3.188em, 1000.49em, 4.194em, -999.979em); top: -4.021em; left: 0.841em;"><span class="mrow" id="MathJax-Span-1228"><span class="mn" id="MathJax-Span-1229" style="font-family: MathJax_Main;">3</span></span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.58em, 1000.49em, 3.971em, -999.979em); top: -4.524em; left: 0.841em;"><span style="font-family: MathJax_Main;">–</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.077em, 1000.88em, 4.418em, -999.979em); top: -4.077em; left: 0em;"><span style="font-family: MathJax_Main;">√</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-1230" style="font-family: MathJax_Main; padding-left: 0.282em;">:</span><span class="mi" id="MathJax-Span-1231" style="font-family: MathJax_Math-italic; padding-left: 0.282em;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.269em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn></msqrt><mo>:</mo><mi>π</mi></math></span></span><script type="math/tex" id="MathJax-Element-92">\sqrt3:\pi</script></label></td></tr>
</tbody></table>
</td>
</tr>
<tr>
<td>
<table class="odpovedi">
<tbody><tr>
<td class="licha dvojita"><input name="15" id="odp15a" type="radio" value="1"><label for="odp15a">a</label></td>
<td> </td>
<td class="licha dvojita"><input name="15" id="odp15b" type="radio" value="2"><label for="odp15b">b</label></td>
</tr>
<tr>
<td> </td>
<td class="licha dvojita"><input name="15" id="odp15c" type="radio" value="3"><label for="odp15c">c</label></td>
<td> </td>
</tr>
<tr>
<td class="licha dvojita"><input name="15" id="odp15d" type="radio" value="4"><label for="odp15d">d</label></td>
<td> </td>
<td class="licha dvojita"><input name="15" id="odp15e" type="radio" value="5"><label for="odp15e">e</label></td>
</tr>
</tbody></table>
2 body
</td>
<td>
<table class="otazky">
<tbody><tr><td>15. Rovnice <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-93-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>=</mo><mn>0</mn></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1232" style="width: 7.883em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.43em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.176em, 1006.41em, 2.406em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1233"><span class="texatom" id="MathJax-Span-1234"><span class="mrow" id="MathJax-Span-1235"><span class="msubsup" id="MathJax-Span-1236"><span style="display: inline-block; position: relative; width: 1.009em; height: 0px;"><span style="position: absolute; clip: rect(3.412em, 1000.54em, 4.194em, -999.979em); top: -4.021em; left: 0em;"><span class="mi" id="MathJax-Span-1237" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; top: -4.356em; left: 0.562em;"><span class="mn" id="MathJax-Span-1238" style="font-size: 70.7%; font-family: MathJax_Main;">2</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span></span></span><span class="mo" id="MathJax-Span-1239" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mi" id="MathJax-Span-1240" style="font-family: MathJax_Math-italic; padding-left: 0.226em;">x</span><span class="mo" id="MathJax-Span-1241" style="font-family: MathJax_Main; padding-left: 0.226em;">+</span><span class="mi" id="MathJax-Span-1242" style="font-family: MathJax_Math-italic; padding-left: 0.226em;">a</span><span class="mo" id="MathJax-Span-1243" style="font-family: MathJax_Main; padding-left: 0.282em;">=</span><span class="mn" id="MathJax-Span-1244" style="font-family: MathJax_Main; padding-left: 0.282em;">0</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.133em; border-left: 0px solid; width: 0px; height: 1.231em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>=</mo><mn>0</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-93">{x^2+x+a=0}</script> (s neznámou <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-94-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1245" style="width: 0.729em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.562em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.568em, 1000.49em, 2.35em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1246"><span class="mi" id="MathJax-Span-1247" style="font-family: MathJax_Math-italic;">x</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.065em; border-left: 0px solid; width: 0px; height: 0.685em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span><script type="math/tex" id="MathJax-Element-94">x</script>) má dva různé záporné kořeny právě tehdy, když</td></tr>
<tr><td><label for="odp15a">a) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-95-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>&#x2208;</mo><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mspace width="thinmathspace" /><mfrac><mn>1</mn><mn>4</mn></mfrac><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1248" style="width: 5.312em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.362em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.121em, 1004.29em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1249"><span class="mi" id="MathJax-Span-1250" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-1251" style="font-family: MathJax_Main; padding-left: 0.282em;">∈</span><span class="mo" id="MathJax-Span-1252" style="font-family: MathJax_Main; padding-left: 0.282em;">(</span><span class="mn" id="MathJax-Span-1253" style="font-family: MathJax_Main;">0</span><span class="mo" id="MathJax-Span-1254" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-1255" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mfrac" id="MathJax-Span-1256" style="padding-left: 0.17em;"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.412em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-1257" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.356em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-1258" style="font-size: 70.7%; font-family: MathJax_Main;">4</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mo" id="MathJax-Span-1259" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>∈</mo><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mspace width="thinmathspace"></mspace><mfrac><mn>1</mn><mn>4</mn></mfrac><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-95">a\in(0,\,\frac14)</script></label></td></tr>
<tr><td><label for="odp15b">b) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-96-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>&#x2260;</mo><mn>0</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1260" style="width: 2.909em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.35em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1002.33em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1261"><span class="mi" id="MathJax-Span-1262" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-1263" style="font-family: MathJax_Main; padding-left: 0.282em;">≠</span><span class="mn" id="MathJax-Span-1264" style="font-family: MathJax_Main; padding-left: 0.282em;">0</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.299em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>≠</mo><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-96">a\ne0</script></label></td></tr>
<tr><td><label for="odp15c">c) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-97-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>&gt;</mo><mn>0</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1265" style="width: 2.909em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.35em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.344em, 1002.33em, 2.406em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1266"><span class="mi" id="MathJax-Span-1267" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-1268" style="font-family: MathJax_Main; padding-left: 0.282em;">></span><span class="mn" id="MathJax-Span-1269" style="font-family: MathJax_Main; padding-left: 0.282em;">0</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.133em; border-left: 0px solid; width: 0px; height: 1.026em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>></mo><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-97">a>0</script></label></td></tr>
<tr><td><label for="odp15d">d) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-98-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>&#x2208;</mo><mo stretchy="false">(</mo><mo>&#x2212;</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace" /><mn>0</mn><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1270" style="width: 6.039em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.921em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.288em, 1004.85em, 2.574em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1271"><span class="mi" id="MathJax-Span-1272" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-1273" style="font-family: MathJax_Main; padding-left: 0.282em;">∈</span><span class="mo" id="MathJax-Span-1274" style="font-family: MathJax_Main; padding-left: 0.282em;">(</span><span class="mo" id="MathJax-Span-1275" style="font-family: MathJax_Main;">−</span><span class="mn" id="MathJax-Span-1276" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-1277" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-1278" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mn" id="MathJax-Span-1279" style="font-family: MathJax_Main; padding-left: 0.17em;">0</span><span class="mo" id="MathJax-Span-1280" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.338em; border-left: 0px solid; width: 0px; height: 1.367em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>∈</mo><mo stretchy="false">(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mspace width="thinmathspace"></mspace><mn>0</mn><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-98">a\in(-1,\,0)</script></label></td></tr>
<tr><td><label for="odp15e">e) <span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-99-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>&#x2208;</mo><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mspace width="thinmathspace" /><mfrac><mn>1</mn><mn>8</mn></mfrac><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1281" style="width: 5.312em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.362em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.121em, 1004.29em, 2.741em, -999.979em); top: -2.177em; left: 0em;"><span class="mrow" id="MathJax-Span-1282"><span class="mi" id="MathJax-Span-1283" style="font-family: MathJax_Math-italic;">a</span><span class="mo" id="MathJax-Span-1284" style="font-family: MathJax_Main; padding-left: 0.282em;">∈</span><span class="mo" id="MathJax-Span-1285" style="font-family: MathJax_Main; padding-left: 0.282em;">(</span><span class="mn" id="MathJax-Span-1286" style="font-family: MathJax_Main;">0</span><span class="mo" id="MathJax-Span-1287" style="font-family: MathJax_Main;">,</span><span class="mspace" id="MathJax-Span-1288" style="height: 0em; vertical-align: 0em; width: 0.17em; display: inline-block; overflow: hidden;"></span><span class="mfrac" id="MathJax-Span-1289" style="padding-left: 0.17em;"><span style="display: inline-block; position: relative; width: 0.45em; height: 0px; margin-right: 0.115em; margin-left: 0.115em;"><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -4.412em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-1290" style="font-size: 70.7%; font-family: MathJax_Main;">1</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(3.412em, 1000.32em, 4.194em, -999.979em); top: -3.63em; left: 50%; margin-left: -0.165em;"><span class="mn" id="MathJax-Span-1291" style="font-size: 70.7%; font-family: MathJax_Main;">8</span><span style="display: inline-block; width: 0px; height: 4.027em;"></span></span><span style="position: absolute; clip: rect(0.841em, 1000.49em, 1.232em, -999.979em); top: -1.283em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.45em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.065em;"></span></span></span></span><span class="mo" id="MathJax-Span-1292" style="font-family: MathJax_Main;">)</span></span><span style="display: inline-block; width: 0px; height: 2.182em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.542em; border-left: 0px solid; width: 0px; height: 1.708em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>∈</mo><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mspace width="thinmathspace"></mspace><mfrac><mn>1</mn><mn>8</mn></mfrac><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-99">a\in(0,\,\frac18)</script></label></td></tr>
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