View of /trunk/NationalProblemLibrary/272/setStewart14_3/stefi14_3.pg

    1 ## DESCRIPTION
    2 ##   Find Partial Derivatives
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Multivariable', 'Partial Derivative', 'Implicit')
    6 ## Tagged by nhamblet
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Partial Derivatives')
   10 ## DBsection('Partial Derivatives')
   11 ## Date('6/2/2000')
   12 ## Author('Joseph Neisendorfer')
   13 ## Institution('University of Rochester')
   14 ## TitleText1('Calculus')
   15 ## EditionText1('')
   16 ## AuthorText1('Stewart')
   17 ## Section1('14.3')
   18 ## Problem1('')
   19 
   20 DOCUMENT();
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a = random(-5, 5);
   34 $b = random(-5, 5);
   35 
   36 $dzdx = - $a;
   37 $dzdy = - $b;
   38 
   39 BEGIN_TEXT
   40 $PAR
   41 If \( \sin(${a}x + ${b}y + z) = 0 \), use implicit differentiation to find the first partial derivatives \(
   42 \frac{\partial z}{\partial x} \) and \( \frac{\partial z}{\partial y} \) at the point (0, 0, 0).
   43 $PAR
   44 A. \( \frac{\partial z}{\partial x}(0, 0, 0) = \) \{ ans_rule(30) \}
   45 $PAR
   46 B. \( \frac{\partial z}{\partial y}(0, 0, 0) = \) \{ ans_rule(30) \}
   47 END_TEXT
   48 ANS(num_cmp($dzdx));
   49 ANS(num_cmp($dzdy));
   50 
   51 ENDDOCUMENT();