View of /trunk/NationalProblemLibrary/UVA-Stew5e/setUVA-Stew5e-C04S04-LHop/4-4-57.pg

    1 ## DESCRIPTION
    2 ##  Calculus: Indeterminant Forms and L'Hopital's Rule
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Indeterminant Forms', 'LHopitals rule')
    6 ## Tagged by YL
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Applications of Differentiation')
   10 ## DBsection('Indeterminate Forms and L'Hospital's Rule')
   11 ## Date('5/29/2005')
   12 ## Author('Jeff Holt')
   13 ## Institution('UVA')
   14 ## TitleText1('Calculus')
   15 ## EditionText1('5e')
   16 ## AuthorText1('Stewart')
   17 ## Section1('4.4')
   18 ## Problem1('57')
   19 
   20 
   21 DOCUMENT();
   22 # This should be the first executable line in the problem.
   23 
   24 loadMacros(
   25 "PG.pl",
   26 "PGbasicmacros.pl",
   27 "PGchoicemacros.pl",
   28 "PGanswermacros.pl",
   29 "PGauxiliaryFunctions.pl"
   30 );
   31 
   32 TEXT(beginproblem());
   33 $showPartialCorrectAnswers = 1;
   34 
   35 $a = random(2,7,1);
   36 $b = random(2,7,1);
   37 $c = exp(-$a*$b);
   38 
   39 TEXT(EV2(<<EOT));
   40 $BR
   41 Evaluate the following limit:
   42 \[ \lim_{ x \rightarrow 0 } (1 - $a x)^{\frac{$b}{x}} \]
   43 Enter $BBOLD -I $EBOLD if your answer is \(-\infty\), enter $BBOLD I $EBOLD if your answer is
   44 \(\infty\), and enter $BBOLD DNE $EBOLD if the limit does not exist.
   45 $PAR
   46 $BR
   47 Limit = \{ans_rule(25) \}
   48 $BR
   49 EOT
   50 
   51 $ans = $c;
   52 ANS(num_cmp($ans, strings=>["-I","I","DNE"]));
   53 
   54 ENDDOCUMENT();
   55 # This should be the last executable line in the problem.