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    1 ##KEYWORDS('parametric equation', 'first derivative', 'second derivative')##DESCRIPTION
2 ## Take derivative on a parametric curve
3 ##ENDDESCRIPTION
4
5 ## Shotwell cleaned
6
7 ## DBsubject('Calculus')
8 ## DBchapter('Parametric Equations and Polar Coordinates')
9 ## DBsection('Tangents and Areas')
10 ## Date('6/3/2002')
11 ## Author('')
12 ## Institution('')
13 ## TitleText1('Calculus: Early Transcendentals')
14 ## EditionText1('4')
15 ## AuthorText1('Stewart')
16 ## Section1('10.2')
17 ## Problem1('15')
18
19 DOCUMENT();        # This should be the first executable line in the problem.
20
22 "PGbasicmacros.pl",
24 "PGauxiliaryFunctions.pl"
25 );
26
27 TEXT(beginproblem());
28 $showPartialCorrectAnswers = 1; 29 30$a = random(2,9,1);
31
32
33 BEGIN_TEXT
34 Given $$x = \sin a t$$ and $$y = \cos a t$$, find the following derivatives
35 as functions of $$t$$ .
36 $BR$BR
37 $$dy/dx=$$ \{ans_rule( 35) \}
38 $BR$BR
39 $$d^2y/dx^2=$$ \{ans_rule( 35) \}
40 END_TEXT
41
42 $soln1 = "-tan($a*t)";
43 $soln2 = "-1/cos($a*t)^3";
44
45 ANS(fun_cmp($soln1,vars=>['t'])); 46 ANS(fun_cmp($soln2,vars=>['t']));
47
48 ENDDOCUMENT();        # This should be the last executable line in the problem.