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| <h2>Difference Quotients as Student Answers</h2>
| | #REDIRECT [[DifferenceQuotient1]] |
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| <!-- Header for these sections -- no modification needed -->
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| <p style="background-color:#eeeeee;border:black solid 1px;padding:3px;">
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| <em>This PG code shows how to check student answers that fully reduced difference quotients for limits that compute derivatives.</em>
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| </p>
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| <p style="text-align:center;">
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| [[IndexOfProblemTechniques|Problem Techniques Index]] | |
| </p>
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| <table cellspacing="0" cellpadding="2" border="0">
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| <tr valign="top">
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| <th> PG problem file </th>
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| <th> Explanation </th>
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| </tr>
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| <!-- Load specialized macro files section -->
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| <tr valign="top">
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| <td style="background-color:#ddffdd;border:black 1px dashed;">
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| <pre>
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| DOCUMENT();
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| loadMacros(
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| "PGstandard.pl",
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| "MathObjects.pl",
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| "parserDifferenceQuotient.pl",
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| );
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| TEXT(beginproblem());
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| </pre>
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| </td>
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| <td style="background-color:#ccffcc;padding:7px;">
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| <p>
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| <b>Initialization:</b>
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| We need to include the macros file <code>parserDifferenceQuotient.pl</code>.
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| </p>
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| </td>
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| </tr>
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| <!-- Setup section -->
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| <tr valign="top">
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| <td style="background-color:#ffffdd;border:black 1px dashed;">
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| <pre>
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| Context("Numeric");
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| $limit = DifferenceQuotient("2*x+h","h");
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| $fp = Compute("2 x");
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| </pre>
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| </td>
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| <td style="background-color:#ffffcc;padding:7px;">
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| <p>
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| <b>Setup:</b>
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| The routine <code>DifferenceQuotient("function","variable")</code> takes the simplified function and a variable name. If the variable is omitted, <code>dx</code> is used by default.
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| </p>
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| <p>
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| If the student enters an unsimplified answer such as
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| <code>((x+h)^2-x^2)/h</code>, their answer will not be marked correct and they will receive the message
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| <i>It looks like you didn't finish simplifying your answer</i>.
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| </p>
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| </td>
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| </tr>
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| <!-- Question text section -->
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| <tr valign="top">
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| <td style="background-color:#ffdddd;border:black 1px dashed;">
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| <pre>
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| Context()->texStrings;
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| BEGIN_TEXT
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| Simplify and then evaluate the limit.
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| $BR
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| $BR
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| \( \displaystyle
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| \frac{d}{dx} \big( x^2 \big)
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| =
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| \lim_{h \to 0} \frac{(x+h)^2-x^2}{h}
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| =
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| \lim_{h \to 0}
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| \big(
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| \)
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| \{ ans_rule(15) \}
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| \( \big) = \)
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| \{ ans_rule(15) \}
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| END_TEXT
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| Context()->normalStrings;
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| </pre>
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| <td style="background-color:#ffcccc;padding:7px;">
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| <p>
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| <b>Main Text:</b>
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| The problem text section of the file is as we'd expect.
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| </p>
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| </td>
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| </tr>
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| <!-- Answer section -->
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| <tr valign="top">
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| <td style="background-color:#eeddff;border:black 1px dashed;">
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| <pre>
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| $showPartialCorrectAnswers = 1;
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| $showPartialCorrectAnswers = 1;
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| ANS( $limit->cmp() );
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| ANS( $fp->cmp() );
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| ENDDOCUMENT();
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| </pre>
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| <td style="background-color:#eeccff;padding:7px;">
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| <p>
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| <b>Answer Evaluation:</b>
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| As is the answer.
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| </p>
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| </td>
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| </tr>
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| </table>
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| <p style="text-align:center;">
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| [[IndexOfProblemTechniques|Problem Techniques Index]]
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| </p>
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| [[Category:Problem Techniques]]
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| <ul>
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| <li>POD documentation: [http://webwork.maa.org/doc/cvs/pg_CURRENT/macros/parserDifferenceQuotient.pl.html parserDifferenceQuotient.pl.html]</li>
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| <li>PG macro: [http://cvs.webwork.rochester.edu/viewcvs.cgi/pg/macros/parserDifferenceQuotient.pl parserDifferenceQuotient.pl]</li>
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| </ul>
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