Difference between revisions of "DifferenceQuotients"

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

Latest revision as of 14:12, 22 June 2015