View of /trunk/NationalProblemLibrary/UVA-Stew5e/setUVA-Stew5e-C03S06-ImplicitDiff/3-6-46.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('46')
   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(
   29 "PG.pl",
   30 "PGbasicmacros.pl",
   31 "PGchoicemacros.pl",
   32 "PGanswermacros.pl",
   33 "PGauxiliaryFunctions.pl"
   34 );
   35 
   36 TEXT(beginproblem());
   37 $showPartialCorrectAnswers = 1;
   38 
   39 $a1 = random(2,8,1);
   40 $b1 = random(2,8,1);
   41 $c1 = random(2,4,1);
   42 
   43 $funct1 = "$a1*$b1*$c1*cos($c1*x)/(1+$b1*$b1*(sin($c1*x))**2)";
   44 
   45 TEXT(EV2(<<EOT));
   46 If \( f(x) = $a1 \arctan($b1 \sin($c1 x) ) \), find \( f'( x ) \).
   47 $BR $BR \{ans_rule(50) \}
   48 $BR
   49 EOT
   50 
   51 $ans = $funct1;
   52 ANS(fun_cmp($ans));
   53 
   54 ENDDOCUMENT();        # This should be the last executable line in the problem.