## DESCRIPTION ## Differential calculus: difference quotients ## ENDDESCRIPTION ## KEYWORDS('differential calculus', 'difference quotients') ## DBsubject('WeBWorK') ## DBchapter('WeBWorK Tutorial') ## DBsection('Fort Lewis Tutorial 2011') ## Date('01/30/2011') ## Author('Paul Pearson') ## Institution('Fort Lewis College') ## TitleText1('') ## EditionText1('') ## AuthorText1('') ## Section1('') ## Problem1('') ########################### # Initialization DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "parserDifferenceQuotient.pl", ); TEXT(beginproblem()); ########################### # Setup Context("Numeric"); $limit = DifferenceQuotient("2*x+h","h");$fp = Compute("2 x"); ########################### # Main text 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; ############################ # Answer evaluation $showPartialCorrectAnswers = 1; ANS($limit->cmp() ); ANS( $fp->cmp() ); ############################ # Solution Context()->texStrings; BEGIN_SOLUTION${PAR}SOLUTION:\${PAR} Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT('MathObject version.'); ENDDOCUMENT();