View of /trunk/NationalProblemLibrary/ASU-topics/setContinuity/4-1-28.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('calculus','continuity')
    6 ## Tagged by YL
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Limits and Derivatives')
   10 ## DBsection('Continuity')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('5e')
   16 ## AuthorText1('Stewart')
   17 ## Section1('2.5')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros("PG.pl",
   23            "PGbasicmacros.pl",
   24            "PGchoicemacros.pl",
   25            "PGanswermacros.pl",
   26            "PGauxiliaryFunctions.pl");
   27 
   28 $b = random(1,5,1);
   29 $bs = $b**2;
   30 $a = random(1,8,1);
   31 
   32 TEXT(beginproblem());
   33 
   34 $showPartialCorrectAnswers = 0;
   35 
   36 
   37 
   38 TEXT(EV3(<<'EOT'));
   39 Let
   40 \[ f(x) = \frac{x^2 + $bs}{$bs - x^2}. \]
   41 Find each point of discontinuity of \(f\), and for each
   42 give the value of the point of discontinuity and evaluate the
   43 indicated one-sided limits.
   44 $PAR
   45 $PAR
   46 $BBOLD NOTE: $EBOLD
   47 When using interval notation in WeBWorK, remember
   48 that:
   49 $BR $SPACE You use 'INF' for \(\infty\) and '-INF' for \(-\infty\).
   50 $BR $SPACE If you have more than one point, give them in
   51 numerical order, from smallest to largest.
   52 $BR $SPACE If you have extra boxes, fill each in with an 'x'.
   53 $BR
   54 $BR
   55 Point 1: \(C = \) \{ans_rule(10)\}
   56 $BR
   57 \(\displaystyle{\lim_{x \rightarrow C^{-}} f(x)}\) = \{ans_rule(10)\}
   58 $BR
   59 \(\displaystyle{\lim_{x \rightarrow C^{+}} f(x)}\) = \{ans_rule(10)\}
   60 $PAR
   61 $BR
   62 Point 2: \(C = \) \{ans_rule(10)\}
   63 $BR
   64 \(\displaystyle{\lim_{x \rightarrow C^{-}} f(x)}\) = \{ans_rule(10)\}
   65 $BR
   66 \(\displaystyle{\lim_{x \rightarrow C^{+}} f(x)}\) = \{ans_rule(10)\}
   67 $PAR
   68 $BR
   69 Point 3: \(C = \) \{ans_rule(10)\}
   70 $BR
   71 \(\displaystyle{\lim_{x \rightarrow C^{-}} f(x)}\) = \{ans_rule(10)\}
   72 $BR
   73 \(\displaystyle{\lim_{x \rightarrow C^{+}} f(x)}\) = \{ans_rule(10)\}
   74 $PAR
   75 $BR
   76 
   77 EOT
   78 
   79 @answers = (num_cmp(-$b, strings=>["x","INF","-INF"]), num_cmp("-INF", strings=>["x","INF","-INF"]), num_cmp("INF", strings=>["x","INF","-INF"]),
   80            num_cmp($b, strings=>["x","INF","-INF"]), num_cmp("INF", strings=>["x","INF","-INF"]), num_cmp("-INF", strings=>["x","INF","-INF"]),
   81             num_cmp("x", strings=>["x","INF","-INF"]),num_cmp("x", strings=>["x","INF","-INF"]),num_cmp("x", strings=>["x","INF","-INF"]));
   82 
   83 
   84 
   85 
   86 ANS(@answers );
   87 
   88 ENDDOCUMENT();        # This should be the last executable line in the problem.