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    1 ##DESCRIPTION
2 #  Created: 3/2/02
3 #  Authors: Minock
4 #  Stewart 4th ed. Section 10.2
5 #  Find d2y/dx2 for parametric equations.
6 ##ENDDESCRIPTION
7
8 ##KEYWORDS('parametric')
9 ## tcao tagged and PAID on 12-12-2003
10
11 ## DBsubject('Calculus')
12 ## DBchapter('Parametric Equations and Polar Coordinates')
13 ## DBsection('Tangents and Areas')
14 ## Date('6/3/2002')
15 ## Author('')
16 ## Institution('')
17 ## TitleText1('Calculus Early Transcendentals')
18 ## EditionText1('4')
19 ## AuthorText1('Stewart')
20 ## Section1('10.2')
21 ## Problem1('15')
22 DOCUMENT();
23
25 "PG.pl",
26 "PGbasicmacros.pl",
27 "PGchoicemacros.pl",
29 "PGauxiliaryFunctions.pl"
30 );
31
32 TEXT(&beginproblem);
33 $showPartialCorrectAnswers = 1; 34 35$a = random(1,9,1);
36 $b = random(2,9,1); 37$c = random(1,9,1);
38 $d = random(2,5,1); 39$ans = "($d*($d-1)/($b**2))(cos(t)**($d-2))";
40
41 $NO_SPACE = '@{\,}'; 42 43 BEGIN_TEXT 44 45 Find $$\displaystyle \frac{d^2y}{dx^2}$$, as a fuction of $$t$$, for 46 the given the parametric equations: 47 $\begin{array}{r{NO_SPACE}c{NO_SPACE}l} 48 x & = & a - b \cos(t) \cr 49 y & = & c + \cos^{d}(t) 50 \end{array}$ 51 $$\displaystyle \frac{d^2y}{dx^2} =$$ \{ ans_rule(50) \}. 52 53 END_TEXT 54 &ANS(function_cmp($ans, "t"));
55
56 ENDDOCUMENT();
57