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<quiz>
  <question type="stack">
    <name>
      <text>10.0.13 (Finding limits quad over quad)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Find the limit of \(f(x)\) as \(x\) goes to infinity where \[f(x)&nbsp; = {@func@}.\]</p><p>\(\lim_{x \to \infty} f(x) = \) [[input:ans1]]. [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>In this case, notice that we can divide every term in the function by \(x^2\) to get 
\[
{@func@} = \frac{{@aa@} + \frac{{@bb@}}{x} + \frac{{@cc@}}{x^2}}{{@dd@}+ \frac{{@ee@}}{x^2}}
\]
Thus 
\[
\lim\limits_{x \to \infty} {@func@} = \lim\limits_{x \to \infty} \frac{{@aa@} + \frac{{@bb@}}{x} + \frac{{@cc@}}{x^2}}{{@dd@} + \frac{{@ee@}}{x^2}} = \frac{{@aa@}+0+0}{{@dd@}+0} = {@ta1@}
\]
</p>]]></text>
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    <idnumber/>
    <stackversion>
      <text>2020081700</text>
    </stackversion>
    <questionvariables>
      <text>aa:1+rand(10);
bb:1+rand(10);
cc: 1+rand(10);
dd: 1+rand(10);
ee: 1+rand(10);

top: aa*x^2 + bb*x + cc
bot: dd*x^2 + ee

func: top/bot;

ta1: aa/dd;</text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>{@func@} has limit {@ta1@}.</text>
    </questionnote>
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      <text/>
    </questiondescription>
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    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>none</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
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    <matrixparens>[</matrixparens>
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      <name>ans1</name>
      <type>algebraic</type>
      <tans>ta1</tans>
      <boxsize>5</boxsize>
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    </input>
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      <name>prt1</name>
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        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
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    <qtest>
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      <description/>
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        <name>ans1</name>
        <value>ta1</value>
      </testinput>
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    </qtest>
  </question>
</quiz>
