##DESCRIPTION # Created: 3/2/02 # Authors: Minock # Stewart 4th ed. Section 10.2 # Find d2y/dx2 for parametric equations. ##ENDDESCRIPTION ##KEYWORDS('parametric') ## tcao tagged and PAID on 12-12-2003 ## DBchapter('Parametric Equations and Polar Coordinates') ## DBsection('Tangents and Areas') ## Date('6/3/2002') ## Author('') ## Institution('') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('10.2') ## Problem1('15') DOCUMENT(); loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(&beginproblem); $showPartialCorrectAnswers = 1;$a = random(1,9,1); $b = random(2,9,1);$c = random(1,9,1); $d = random(2,5,1);$ans = "($d*($d-1)/($b**2))(cos(t)**($d-2))"; $NO_SPACE = '@{\,}'; BEGIN_TEXT Find $$\displaystyle \frac{d^2y}{dx^2}$$, as a fuction of $$t$$, for the given the parametric equations: $\begin{array}{r{NO_SPACE}c{NO_SPACE}l} x & = & a - b \cos(t) \cr y & = & c + \cos^{d}(t) \end{array}$ $$\displaystyle \frac{d^2y}{dx^2} =$$ \{ ans_rule(50) \}. END_TEXT &ANS(function_cmp($ans, "t")); ENDDOCUMENT();