View of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh2S2/UR_VC_5_7.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('vector' 'limit')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Differentiation')
   10 ## DBsection('Partial Derivatives and Continuity')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Dartmouth')
   14 ## TitleText1('Basic Multivariable Calculus')
   15 ## EditionText1('')
   16 ## AuthorText1('Marsden, Tromba, Weinstein')
   17 ## Section1('2.2')
   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(1, 5);
   34 $b = random(1, 5);
   35 $c = random(1, 5);
   36 $d = random(1, 5);
   37 
   38 $ans = ($d * $c * exp($a**2 + $b**2)) / ($a**3 + $b**3 + $c**3);
   39 
   40 BEGIN_TEXT
   41 $PAR
   42 Find the limit, if it exists, or type N if it does not exist.
   43 $PAR
   44 \( \lim_{(x, y, z) \rightarrow ($a, $b, $c)} \frac{${d}ze^{x^2+y^2}}{${a}x^2 +
   45 ${b}y^2 + ${c}z^2} = \) \{ ans_rule(40) \}
   46 END_TEXT
   47 ANS(num_cmp($ans, strings=>['N']));
   48 
   49 ENDDOCUMENT();