DifferenceQuotient1: Difference between revisions

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{{historical}}
<p style="font-size: 120%;font-weight:bold">This problem has been replaced with [https://openwebwork.github.io/pg-docs/sample-problems/DiffCalc/DifferenceQuotient.html a newer version of this problem]</p>
<h2>Answer is a Difference Quotient</h2>
<h2>Answer is a Difference Quotient</h2>


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This PG code shows how to require students to simplify a difference quotient.
This PG code shows how to require students to simplify a difference quotient.
</p>
</p>
* File location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/DiffCalc/DifferenceQuotient1.pg NationalProblemLibrary/FortLewis/Authoring/Templates/DiffCalc/DifferenceQuotient1.pg]
<!--* File location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/DiffCalc/DifferenceQuotient1.pg NationalProblemLibrary/FortLewis/Authoring/Templates/DiffCalc/DifferenceQuotient1.pg] -->
 
* PGML location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/DiffCalc/DifferenceQuotient1_PGML.pg FortLewis/Authoring/Templates/DiffCalc/DifferenceQuotient1_PGML.pg]


<br clear="all" />
<br clear="all" />
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<tr valign="top">
<tr valign="top">
<th> PG problem file </th>
<th style="width: 50%"> PG problem file </th>
<th> Explanation </th>
<th> Explanation </th>
</tr>
</tr>
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loadMacros(
loadMacros(
"PGstandard.pl",
  'PGstandard.pl',
"MathObjects.pl",
  'MathObjects.pl',
"parserDifferenceQuotient.pl",
  'parserDifferenceQuotient.pl',
  'PGML.pl',
  'PGcourse.pl'
);
);
TEXT(beginproblem());
TEXT(beginproblem());
</pre>
</pre>
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<td style="background-color:#ffffdd;border:black 1px dashed;">
<td style="background-color:#ffffdd;border:black 1px dashed;">
<pre>
<pre>
Context("Numeric");
Context('Numeric');


$limit = DifferenceQuotient("2*x+h","h");
$limit = DifferenceQuotient('2*x+h','h');


$fp = Compute("2 x");
$fp = Compute('2 x');
</pre>
</pre>
</td>
</td>
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<td style="background-color:#ffdddd;border:black 1px dashed;">
<td style="background-color:#ffdddd;border:black 1px dashed;">
<pre>
<pre>
Context()->texStrings;
BEGIN_PGML
BEGIN_TEXT
[`` \frac{d}{dx} \big( x^2 \big) = \lim_{h \to 0} \frac{(x+h)^2-x^2}{h}
Simplify and then evaluate the limit.
  = \lim_{h \to 0} \big(``][_______________]{$limit}[`` \big) = ``]
$BR
[_______________]{$fp}
$BR
 
\( \displaystyle
END_PGML
\frac{d}{dx} \big( x^2 \big)  
=
\lim_{h \to 0} \frac{(x+h)^2-x^2}{h}  
=  
\lim_{h \to 0}  
\big(
\)
\{ ans_rule(15) \}
\( \big) = \)
\{ ans_rule(15) \}
END_TEXT
Context()->normalStrings;
</pre>
</pre>
<td style="background-color:#ffcccc;padding:7px;">
<td style="background-color:#ffcccc;padding:7px;">
<p>
<p>
<b>Main Text:</b>
<b>Main Text:</b>
</p>
</td>
</tr>
<!-- Answer evaluation section -->
<tr valign="top">
<td style="background-color:#eeddff;border:black 1px dashed;">
<pre>
$showPartialCorrectAnswers = 1;
ANS( $limit->cmp() );
ANS( $fp->cmp() );
</pre>
<td style="background-color:#eeccff;padding:7px;">
<p>
<b>Answer Evaluation:</b>
</p>
</p>
</td>
</td>
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<td style="background-color:#ddddff;border:black 1px dashed;">
<td style="background-color:#ddddff;border:black 1px dashed;">
<pre>
<pre>
Context()->texStrings;
BEGIN_PGML_SOLUTION
BEGIN_SOLUTION
Solution explanation goes here.
Solution explanation goes here.
END_SOLUTION
END_PGML_SOLUTION
Context()->normalStrings;


COMMENT('MathObject version.');
COMMENT('Uses PGML.');


ENDDOCUMENT();
ENDDOCUMENT();

Latest revision as of 13:19, 28 June 2023

This article has been retained as a historical document. It is not up-to-date and the formatting may be lacking. Use the information herein with caution.

This problem has been replaced with a newer version of this problem

Answer is a Difference Quotient

Click to enlarge

This PG code shows how to require students to simplify a difference quotient.


Templates by Subject Area

PG problem file Explanation

Problem tagging data

Problem tagging: 

DOCUMENT();

loadMacros(
  'PGstandard.pl',
  'MathObjects.pl',
  'parserDifferenceQuotient.pl',
  'PGML.pl',
  'PGcourse.pl'
);
TEXT(beginproblem());

Initialization: We need to include the macros file parserDifferenceQuotient.pl. 

Context('Numeric');

$limit = DifferenceQuotient('2*x+h','h');

$fp = Compute('2 x');

Setup: The routine DifferenceQuotient("function","variable") takes the simplified function and a variable name. If the variable is omitted, dx is used by default. 

BEGIN_PGML
[`` \frac{d}{dx} \big( x^2 \big) = \lim_{h \to 0} \frac{(x+h)^2-x^2}{h}
  = \lim_{h \to 0} \big(``][_______________]{$limit}[`` \big) = ``]
[_______________]{$fp}

END_PGML

Main Text: 

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

COMMENT('Uses PGML.');

ENDDOCUMENT();

Solution:

Templates by Subject Area

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