##DESCRIPTION ## Related rates -- find rate of change of area of a circle given ## the rate of change of radius and value of radius. ##ENDDESCRIPTION ## Shotwell cleaned ## tcao , PAID on 11-24-2003 ## DBsubject(Calculus - single variable) ## DBchapter(Applications of differentiation) ## DBsection(Related rates) ## Date(6/3/2002) ## Institution(Univeristy of Utah) ## Author(Utah ww group) ## Level(3) ## TitleText1('Calculus: Early Transcendentals') ## AuthorText1('Stewart') ## EditionText1('6') ## Section1('3.9') ## Problem1('5') ## TitleText2('Calculus: Early Transcendentals') ## AuthorText2('Rogawski') ## EditionText2('1') ## Section2('3.11') ## Problem2('5') ## TitleText3('Calculus I') ## AuthorText3('Jerrold Marsden and Alan Weinstein') ## EditionText3('2') ## Section3('Rates of Change and the Chain Rule') ## Problem3('') ## TitleText4('Calculus') ## AuthorText4('Dale Varberg, Edwin J. Purcell, and Steven E. Rigdon') ## EditionText4('9') ## Section4('The Derivative') ## Problem4('') ## KEYWORDS('derivatives', 'related rates','Calculus') ##TYPE('word problem') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PGbasicmacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl", "MathObjects.pl", "parserFunctionPrime.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 0; Context("Numeric"); parser::FunctionPrime->Enable(); Context()->variables->add(t=> 'Real'); parserFunction("r(t)" => "15");$r = Formula("r(t)"); $dr = Formula("r'(t)");$dA = Compute("2 pi $r *$dr"); BEGIN_TEXT Let $$A(t)$$ be the area of a circle with radius $$r(t)$$ at time $$t$$, i.e. $$A(t) = \pi[r(t)]^2.$$ Compute $$A'(t)$$ in terms of $$r(t)$$, and $$r'(t)$$. Enter "r(t)" for $$r(t)$$ and "r'(t)" for $$r'(t)$$. $PAR $$A'(t) =$$\{ans_rule(30) \} END_TEXT ANS($dA->cmp); #parser::FunctionPrime->Disable(); ENDDOCUMENT(); # This should be the last executable line in the problem.