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      <text>23.3.2.3 terms in F.Series</text>
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      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
For each of the following functions deduce whether the corresponding Fourier series
contains sine terms only, cosine terms only or both as well as a constant term.<p><br></p><p style="text-align: center;"><img src="@@PLUGINFILE@@/23-3-2-task-figures.svg" alt="different functions" width="514" height="386" class="img-responsive atto_image_button_text-bottom"><br></p><p><br></p>

<b>1)</b> constant term: [[input:ans1]] [[validation:ans1]][[feedback:prt1]]
<p></p>
Other terms: [[input:ans2]][[validation:ans2]][[feedback:prt2]] 
<p></p>
<b>2)</b> Constant term: [[input:ans3]] [[validation:ans3]][[feedback:prt3]]
<p></p>
Other terms: [[input:ans4]] [[validation:ans4]][[feedback:prt4]]<p></p>
<b>3)</b> Constant term: [[input:ans5]] [[validation:ans5]][[feedback:prt5]]
<p></p>
Other terms: [[input:ans6]] [[validation:ans6]][[feedback:prt6]]<p></p>
<b>4)</b> Constant term: [[input:ans7]] [[validation:ans7]][[feedback:prt7]]
<p></p>
Other terms: [[input:ans8]] [[validation:ans8]][[feedback:prt8]]<p></p>
<b>5)</b> Constant term: [[input:ans9]] [[validation:ans9]][[feedback:prt9]]
<p></p>
Other terms: [[input:ans10]] [[validation:ans10]][[feedback:prt10]]<p></p>
<b>6)</b> Constant term: [[input:ans11]] [[validation:ans11]][[feedback:prt11]]
<p></p>
Other terms: [[input:ans12]] [[validation:ans12]][[feedback:prt12]]<p></p>
<b>7)</b> Constant term: [[input:ans13]] [[validation:ans13]][[feedback:prt13]]
<p></p>
Other terms: [[input:ans14]] [[validation:ans14]][[feedback:prt14]]<p></p>]]></text>
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ta2: [["cosine",true],["sine", false], ["both", false]];

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ta4: [["cosine",true],["sine", false], ["both", false]];

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ta10: [["cosine",false],["sine", true], ["both", false]];

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ta12: [["cosine",false],["sine", false], ["both", true]];

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ta14: [["cosine",true],["sine", false], ["both", false]];]]></text>
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    <decimals>.</decimals>
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        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>String</answertest>
        <sans>ans6</sans>
        <tans>first(mcq_correct(ta6))</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt6-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt6-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>prt7</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>String</answertest>
        <sans>ans7</sans>
        <tans>first(mcq_correct(ta7))</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt7-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt7-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>prt8</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>String</answertest>
        <sans>ans8</sans>
        <tans>first(mcq_correct(ta8))</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt8-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt8-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <prt>
      <name>prt9</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>String</answertest>
        <sans>ans9</sans>
        <tans>first(mcq_correct(ta9))</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt9-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt9-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value><![CDATA["yes"]]></value>
      </testinput>
      <testinput>
        <name>ans10</name>
        <value><![CDATA["sine"]]></value>
      </testinput>
      <testinput>
        <name>ans11</name>
        <value><![CDATA["yes"]]></value>
      </testinput>
      <testinput>
        <name>ans12</name>
        <value><![CDATA["both"]]></value>
      </testinput>
      <testinput>
        <name>ans13</name>
        <value><![CDATA["yes"]]></value>
      </testinput>
      <testinput>
        <name>ans14</name>
        <value><![CDATA["cosine"]]></value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value><![CDATA["cosine"]]></value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value><![CDATA["no"]]></value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value><![CDATA["cosine"]]></value>
      </testinput>
      <testinput>
        <name>ans5</name>
        <value><![CDATA["no"]]></value>
      </testinput>
      <testinput>
        <name>ans6</name>
        <value><![CDATA["sine"]]></value>
      </testinput>
      <testinput>
        <name>ans7</name>
        <value><![CDATA["yes"]]></value>
      </testinput>
      <testinput>
        <name>ans8</name>
        <value><![CDATA["cosine"]]></value>
      </testinput>
      <testinput>
        <name>ans9</name>
        <value><![CDATA["no"]]></value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt10</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt10-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt11</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt11-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt12</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt12-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt13</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt13-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt14</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt14-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt3</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt3-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt4</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt4-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt5</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt5-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt6</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt6-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt7</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt7-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt8</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt8-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt9</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt9-1-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value><![CDATA["no"]]></value>
      </testinput>
      <testinput>
        <name>ans10</name>
        <value><![CDATA["cosine"]]></value>
      </testinput>
      <testinput>
        <name>ans11</name>
        <value><![CDATA["no"]]></value>
      </testinput>
      <testinput>
        <name>ans12</name>
        <value><![CDATA["sine"]]></value>
      </testinput>
      <testinput>
        <name>ans13</name>
        <value><![CDATA["no"]]></value>
      </testinput>
      <testinput>
        <name>ans14</name>
        <value><![CDATA["both"]]></value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value><![CDATA["sine"]]></value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value><![CDATA["yes"]]></value>
      </testinput>
      <testinput>
        <name>ans4</name>
        <value><![CDATA["both"]]></value>
      </testinput>
      <testinput>
        <name>ans5</name>
        <value><![CDATA["yes"]]></value>
      </testinput>
      <testinput>
        <name>ans6</name>
        <value><![CDATA["both"]]></value>
      </testinput>
      <testinput>
        <name>ans7</name>
        <value><![CDATA["no"]]></value>
      </testinput>
      <testinput>
        <name>ans8</name>
        <value><![CDATA["sine"]]></value>
      </testinput>
      <testinput>
        <name>ans9</name>
        <value><![CDATA["yes"]]></value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt10</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt10-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt11</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt11-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt12</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt12-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt13</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt13-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt14</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt14-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt2-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt3</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt3-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt4</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt4-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt5</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt5-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt6</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt6-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt7</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt7-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt8</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt8-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt9</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt9-1-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
