View of /trunk/NationalProblemLibrary/UVA-Stew5e/setUVA-Stew5e-C03S06-ImplicitDiff/3-6-27.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('27')
   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 $a = random(5,7,1);
   40 $x1 = random(1,4,1);
   41 $y1 = (($x1**(3))*($a - $x1))**(1/2);
   42 $m1 = ((3*($x1**(2))*($a - $x1)) - ($x1**(3)))/(2*$y1);
   43 
   44 TEXT(EV2(<<EOT));
   45 Find the equation of the tangent line to the curve (a piriform)
   46  \( y^{2} = x^{3} ($a - x) \)
   47 at the point \( ( $x1 , $y1 ) \).
   48 The equation of this tangent line can be written in the form \( y = mx+b \)
   49 where \( m \) is: \{ans_rule(30) \}
   50 $BR
   51 EOT
   52 $ans = $m1;
   53 ANS(num_cmp($ans));
   54 
   55 TEXT(EV2(<<EOT));
   56 and  where \( b \) is: \{ans_rule(30) \}
   57 $BR
   58 EOT
   59 $ans = $y1 -$m1*$x1;
   60 ANS(num_cmp($ans));
   61 
   62 ENDDOCUMENT();        # This should be the last executable line in the problem.