DifferenceQuotients

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
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "parserDifferenceQuotient.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. 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.
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;	Main Text: The problem text section of the file is as we'd expect.
$showPartialCorrectAnswers = 1; $showPartialCorrectAnswers = 1; ANS( $limit->cmp() ); ANS( $fp->cmp() ); ENDDOCUMENT();	Answer Evaluation: As is the answer.

Problem Techniques Index

• POD documentation: [parserDifferenceQuotient.pl.html]
• PG macro: [parserDifferenceQuotient.pl]