View of /trunk/NationalProblemLibrary/UVA-Stew5e/setUVA-Stew5e-C03S06-ImplicitDiff/3-6-17.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('17')
   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            "PGanswermacros.pl",
   31 "PGauxiliaryFunctions.pl");
   32 
   33 TEXT(beginproblem());
   34 $showPartialCorrectAnswers = 0;
   35 
   36 $pi = $PI;
   37 $a = random(3,7,2);
   38 $b = random(2,6,1);
   39 $x1 = $a*($pi/2);
   40 $y1 = $b*($pi);
   41 $c = random(3,5,2);
   42 $d = random(2,4);
   43 $f = cos(($c*$x1) - ($d*$y1)) - $x1*(exp(-$x1));
   44 $num = -$x1*(exp(-$x1)) + exp(-$x1) + $c*(sin($c*$x1 - $d*$y1));
   45 $denom = $d*(sin($c*$x1 - $d*$y1));
   46 
   47 while ( $denom == 0 ) {
   48 $x1 = random(1,8);
   49 $y1 = random(1,8);
   50 $denom = $d*(sin($c*$x1 - $d*$y1));
   51 }
   52 
   53 
   54 # Present the text.
   55 BEGIN_TEXT
   56 Find the slope of the tangent line to the curve
   57 
   58 \[ \cos($c x - $d y)  - x e^{-x}  = -\frac{$a \pi}{2} e^{- $a \pi/2} \]
   59 
   60 at the point \( ( $a\pi/2,$b\pi ) \). $BR
   61 \{ &ans_rule(50) \}
   62 END_TEXT
   63 
   64 ANS(num_cmp("$num/$denom") );
   65 
   66 ENDDOCUMENT();        # This should be the last executable line in the problem.