View of /trunk/NationalProblemLibrary/ASU-topics/setContinuity/4-1-31.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 ## TitleText2('Calculus: Early Transcendentals')
   21 ## EditionText2('6')
   22 ## AuthorText2('Stewart')
   23 ## Section2('2.5')
   24 ## Problem2('')
   25 ## TitleText3('Calculus: Early Transcendentals')
   26 ## EditionText3('1')
   27 ## AuthorText3('Rogawski')
   28 ## Section3('2.4')
   29 ## Problem3('27')
   30 
   31 DOCUMENT();        # This should be the first executable line in the problem.
   32 
   33 loadMacros("PG.pl",
   34            "PGbasicmacros.pl",
   35            "PGchoicemacros.pl",
   36            "PGanswermacros.pl",
   37            "PGauxiliaryFunctions.pl");
   38 
   39 $a = random(2,8,1);
   40 $b = random(1,3,1);
   41 $c = random(4,7,1);
   42 $ab = -$a*$b;
   43 $c2 = -2*$c;
   44 $cs = $c**2;
   45 
   46 TEXT(beginproblem());
   47 
   48 $showPartialCorrectAnswers = 0;
   49 
   50 
   51 TEXT(EV3(<<'EOT'));
   52 Let
   53 \[ f(x) = \frac{$a x ? {$ab}}{x^4 ? {$c2} x^3 ? {$cs}x^2}. \]
   54 Find each point of discontinuity of \(f\), and for each
   55 give the value of the point of discontinuity and evaluate the
   56 indicated one-sided limits.
   57 $PAR
   58 $PAR
   59 $BBOLD NOTE: $EBOLD
   60 When using interval notation in WeBWorK, remember
   61 that:
   62 $BR $SPACE You use 'INF' for \(\infty\) and '-INF' for \(-\infty\).
   63 $BR $SPACE If you have more than one point, give them in
   64 numerical order, from smallest to largest.
   65 $BR $SPACE If you have extra boxes, fill each in with an 'x'.
   66 $BR
   67 $BR
   68 Point 1: \(C = \) \{ans_rule(10)\}
   69 $BR
   70 \(\displaystyle{\lim_{x \rightarrow C^{-}} f(x)}\) = \{ans_rule(10)\}
   71 $BR
   72 \(\displaystyle{\lim_{x \rightarrow C^{+}} f(x)}\) = \{ans_rule(10)\}
   73 $PAR
   74 $BR
   75 Point 2: \(C = \) \{ans_rule(10)\}
   76 $BR
   77 \(\displaystyle{\lim_{x \rightarrow C^{-}} f(x)}\) = \{ans_rule(10)\}
   78 $BR
   79 \(\displaystyle{\lim_{x \rightarrow C^{+}} f(x)}\) = \{ans_rule(10)\}
   80 $PAR
   81 $BR
   82 Point 3: \(C = \) \{ans_rule(10)\}
   83 $BR
   84 \(\displaystyle{\lim_{x \rightarrow C^{-}} f(x)}\) = \{ans_rule(10)\}
   85 $BR
   86 \(\displaystyle{\lim_{x \rightarrow C^{+}} f(x)}\) = \{ans_rule(10)\}
   87 $PAR
   88 $BR
   89 
   90 EOT
   91 
   92 @answers = (num_cmp(0, strings=>["x","INF","-INF"]),num_cmp("-INF", strings=>["x","INF","-INF"]),num_cmp("-INF", strings=>["x","INF","-INF"]),
   93             num_cmp($c, strings=>["x","INF","-INF"]),num_cmp("INF", strings=>["x","INF","-INF"]),num_cmp("INF", strings=>["x","INF","-INF"]),
   94             num_cmp("x", strings=>["x","INF","-INF"]),num_cmp("x", strings=>["x","INF","-INF"]),num_cmp("x", strings=>["x","INF","-INF"]));
   95 
   96 
   97 
   98 
   99 ANS(@answers );
  100 
  101 ENDDOCUMENT();        # This should be the last executable line in the problem.