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

Tue Jul 10 12:42:27 2007 UTC (5 years, 10 months ago) by jjholt
File size: 2367 byte(s)
Fixed Tags. --JJH

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
23            "PGbasicmacros.pl",
24            "PGchoicemacros.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"]));
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