Difference between revisions of "DifferenceQuotients"

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(New page: <h2>Difference Quotients as Student Answers</h2> <!-- Header for these sections -- no modification needed --> <p style="background-color:#eeeeee;border:black solid 1px;padding:3px;"> ...)
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[[Category:Problem Techniques]]
[[Category:Problem Techniques]]
<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>

Revision as of 23:14, 22 April 2010

Difference Quotients as Student Answers

This PG code shows how to check student answers that fully reduced difference quotients for limits that compute derivatives.

Problem Techniques Index

PG problem file Explanation



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


$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.

If the student enters an unsimplified answer such as ((x+h)^2-x^2)/h, their answer will not be marked correct and they will receive the message It looks like you didn't finish simplifying your answer.

Simplify and then evaluate the limit.
\( \displaystyle 
\frac{d}{dx} \big( x^2 \big) 
\lim_{h \to 0} \frac{(x+h)^2-x^2}{h} 
\lim_{h \to 0} 
\{ ans_rule(15) \}
\( \big) = \)
\{ ans_rule(15) \}

Main Text: The problem text section of the file is as we'd expect.

$showPartialCorrectAnswers = 1;

$showPartialCorrectAnswers = 1;

ANS( $limit->cmp() );
ANS( $fp->cmp() );


Answer Evaluation: As is the answer.

Problem Techniques Index