View of /trunk/NationalProblemLibrary/UVA-Stew5e/setUVA-Stew5e-C03S06-ImplicitDiff/3-6-20.pg

    1 ##DESCRIPTION
    2 ##Calculus: Differentiation
    3 ##ENDDESCRIPTION
    4 
    5 ##KEYWORDS('calculus', 'differentiation')
    6 ##Tagged by YJ
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Differentiation')
   10 ## DBsection('Implicit Differentiation')
   11 ## Date('5/26/2005')
   12 ## Author('Jeff Holt')
   13 ## Institution('UVA')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('3.6')
   18 ## Problem1('20')
   19 
   20 ## TitleText2('Calculus: Early Transcendentals')
   21 ## EditionText2('6')
   22 ## AuthorText2('Stewart')
   23 ## Section2('3.5')
   24 ## Problem2('')
   25 
   26 DOCUMENT();        # This should be the first executable line in the problem.
   27 
   28 loadMacros("PG.pl",
   29            "PGbasicmacros.pl",
   30            "PGchoicemacros.pl",
   31            "PGanswermacros.pl",
   32 "PGauxiliaryFunctions.pl");
   33 
   34 TEXT(beginproblem());
   35 $showPartialCorrectAnswers = 0;
   36 
   37 $pi = $PI;
   38 $a = random(3,7,1);
   39 $b = random(3,7,2);
   40 $x1 = $a*($pi);
   41 $y1 = $b*($pi/2);
   42 $c = random(2,6,1);
   43 $d = random(2,6,1);
   44 $f = random(2,6,1);
   45 $g = $c*sin($x1) + $d*cos($y1) - $f*sin($x1)*cos($y1) + $x1;
   46 $num = ($f*cos($x1)*cos($y1)) - ($c*cos($x1)) - 1;
   47 $denom = ($f*sin($x1)*sin($y1)) - ($d*sin($y1));
   48 
   49 
   50 
   51 $yp =  $num/$denom;
   52 
   53 # Present the text.
   54 TEXT(EV2(<<EOT));
   55 Find the slope of the tangent line to the curve
   56 
   57 \[ $c \sin(x) + $d \cos(y) - $f \sin(x) \cos(y) + x = {$a \pi} \]
   58 
   59 at the point \( ( $a\pi,$b\pi/2 ) \). $BR
   60 \{ &ans_rule(50) \}
   61 EOT
   62 
   63 ANS(num_cmp($yp));
   64 
   65 ENDDOCUMENT();        # This should be the last executable line in the problem.