View of /trunk/NationalProblemLibrary/Dartmouth/setStewartCh15S2/problem_3.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('limit')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Partial Derivatives')
   10 ## DBsection('Limits and Continuity')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Dartmouth')
   14 ## TitleText1('Calculus')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('15.2')
   18 ## Problem1('')
   19 
   20 DOCUMENT();
   21 loadMacros("PG.pl",
   22            "PGbasicmacros.pl",
   23            "PGchoicemacros.pl",
   24            "PGanswermacros.pl",
   25            "PGauxiliaryFunctions.pl",
   26            "PGgraphmacros.pl",
   27            "Dartmouthmacros.pl");
   28 
   29 
   30 ## Do NOT show partial correct answers
   31 $showPartialCorrectAnswers = 0;
   32 
   33 $a = random(2,9)*non_zero_random(-1,1);
   34 $b = random(2,9)*non_zero_random(-1,1);
   35 
   36 
   37 ## Ok, we are ready to begin the problem...
   38 ##
   39 TEXT(beginproblem());
   40 
   41 
   42 BEGIN_TEXT
   43 $BR
   44 
   45 Find the limit
   46 \[
   47     \lim_{(x,y) \to (0, 0)}
   48 \frac{($a x^2 + $b y^2)}{\sqrt{($a x^2 + $b y^2 +1)} -1}
   49 \]
   50     \{ans_rule()\}  (Enter dne if the limit does not exist)
   51 $PAR
   52 END_TEXT
   53 
   54     ANS(num_cmp("2"));
   55 
   56 ENDDOCUMENT();
   57 
   58 
   59 
   60