View of /trunk/NationalProblemLibrary/UVA-Stew5e/setUVA-Stew5e-C03S06-ImplicitDiff/3-6-15.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('15')
   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 = 0;
   38 install_problem_grader(~~&std_problem_grader);
   39 
   40 $a1 = random(2,7,1);
   41 $b1 = random(2,7,1);
   42 
   43 $questStr1 =EV2( " \( $a1 \sin (x-y) = $b1 y \sin x \)");
   44 $ansStr1 =EV2( "\( \frac {$a1 \cos (x-y) - $b1 y \cos x } {$a1 \cos (x-y) + $b1 \sin x } \)");
   45 
   46 $questStr2 = EV2(" \( $a1 \sin (x-y) = $b1 y \cos x \)");
   47 $ansStr2 =EV2( "\( \frac {$a1 \cos (x-y) + $b1 y \sin x } {$a1 \cos (x-y) + $b1 \cos x } \)");
   48 $questStr3 = EV2(" \( $a1 \cos (x-y) = $b1 y \sin x \)");
   49 $ansStr3 = EV2("\( \frac {-$a1 \sin (x-y) - $b1 y \cos x } {$b1 \sin x - $a1 \sin (x-y) } \)");
   50 
   51 $questStr4 =EV2( " \( $a1 \cos (x-y) = $b1 y \cos x \)");
   52 $ansStr4 = EV2("\( \frac {-$a1 \sin (x-y) + $b1 y \sin x } {$b1 \cos x - $a1 \sin (x-y) } \)");
   53 
   54 @questions =( $questStr1,$questStr2,$questStr3,$questStr4);
   55 @answers =( $ansStr1,$ansStr2,$ansStr3,$ansStr4);
   56 
   57 # Now randomize the questions:
   58 @slice = &NchooseK(4,4);
   59 @shuffle = &shuffle(scalar(@slice));
   60 #############################################################################
   61 
   62 TEXT(EV2(<<EOT));
   63 Find \( y' \) by implicit differentiation.  Match the expressions defining
   64 \( y \) implicitly with the letters labeling the
   65 expressions for  \( y' \).
   66 EOT
   67 TEXT(
   68 &match_questions_list(@questions[@slice]),
   69 &OL(@answers[@slice[@shuffle]])
   70 );
   71 ANS(str_cmp([@ALPHABET[&invert(@shuffle)]], filters=>["remove_whitespace","ignore_case"]));
   72      ##the correct answers are obtained by applying
   73      ##the inverse (adjoint) permutation to the captions.
   74 
   75 ENDDOCUMENT();        # This should be the last executable line in the problem.