View of /trunk/NationalProblemLibrary/ma123DB/set8/s10_2_15.pg

    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 
   21 loadMacros(
   22 "PGbasicmacros.pl",
   23 "PGanswermacros.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.