Difference between revisions of "DifferenceQuotient1"

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(added historical tag and gave updated problem link)
 
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{{historical}}
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<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problem has been replaced with [https://openwebwork.github.io/pg-docs/sample-problems/DiffCalc/DifferenceQuotient.html a newer version of this problem]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>
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* 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]
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<!--* 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] -->
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* 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">
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<th> PG problem file </th>
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<th style="width: 50%"> PG problem file </th>
 
<th> Explanation </th>
  
<th> Explanation </th>
 
</tr>
  
</tr>
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loadMacros(
  
loadMacros(
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"PGstandard.pl",
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'PGstandard.pl',
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"MathObjects.pl",
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'MathObjects.pl',
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"parserDifferenceQuotient.pl",
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'parserDifferenceQuotient.pl',
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'PGML.pl',
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'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>
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Context("Numeric");
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Context('Numeric');
   
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$limit = DifferenceQuotient("2*x+h","h");
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$limit = DifferenceQuotient('2*x+h','h');
   
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$fp = Compute("2 x");
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$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>
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Context()->texStrings;
  
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BEGIN_PGML
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BEGIN_TEXT
  
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[`` \frac{d}{dx} \big( x^2 \big) = \lim_{h \to 0} \frac{(x+h)^2-x^2}{h}
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Simplify and then evaluate the limit.
  
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= \lim_{h \to 0} \big(``][_______________]{$limit}[`` \big) = ``]
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$BR
  
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[_______________]{$fp}
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$BR
  
  +
−
\( \displaystyle
 
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END_PGML
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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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\{ 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;
  
 
</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>
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</p>
  
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</td>
  
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</tr>
  
−  
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<!-- Answer evaluation 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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ANS( $limit->cmp() );
  
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ANS( $fp->cmp() );
  
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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>
  
 
</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>
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Context()->texStrings;
  
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BEGIN_PGML_SOLUTION
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BEGIN_SOLUTION
  
 
Solution explanation goes here.
  
Solution explanation goes here.
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END_SOLUTION
  
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END_PGML_SOLUTION
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Context()->normalStrings;
  
   
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COMMENT('MathObject version.');
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COMMENT('Uses PGML.');
   
 
ENDDOCUMENT();
  
ENDDOCUMENT();

Latest revision as of 08:19, 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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