View of /trunk/NationalProblemLibrary/UVA-Stew5e/setUVA-Stew5e-C03S06-ImplicitDiff/3-6-29.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('29')
   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 $x1 = random(-3,3,6);
   40 $y1 = random(-1,1,2);
   41 $m1 = (25*$x1-4*$x1*($x1*$x1+$y1*$y1))/(4*($x1*$x1+$y1*$y1)*$y1+25*$y1);
   42 
   43 TEXT(EV2(<<EOT));
   44 Find the equation of the tangent line to the curve (a lemniscate)
   45  \( 2(x^2+y^2)^2 = 25(x^2-y^2) \)
   46 at the point \( ( $x1 , $y1 ) \).
   47 The equation of this tangent line can be written in the form \( y = mx+b \)
   48 where
   49 $PAR
   50 \( m \) = \{ans_rule(30) \}
   51 $BR
   52 EOT
   53 $ans = $m1;
   54 ANS(num_cmp($ans));
   55 
   56 TEXT(EV2(<<EOT));
   57 and
   58 $PAR
   59 \( b \) = \{ans_rule(30) \}
   60 $BR
   61 EOT
   62 $ans = $y1 -$m1*$x1;
   63 ANS(num_cmp($ans));
   64 
   65 ENDDOCUMENT();        # This should be the last executable line in the problem.