View of /trunk/NationalProblemLibrary/maCalcDB/setParametric1Curves/ur_pa_1_5.pg

    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 
   24 loadMacros(
   25 "PG.pl",
   26 "PGbasicmacros.pl",
   27 "PGchoicemacros.pl",
   28 "PGanswermacros.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