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# View of /trunk/NationalProblemLibrary/ASU-topics/setContinuity/4-1-31.pg

Sat Sep 8 05:17:01 2007 UTC (5 years, 8 months ago) by sh002i
File size: 2694 byte(s)
Added tags for Rogawski's "Calculus: Early Transcendentals".


    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
34            "PGbasicmacros.pl",
35            "PGchoicemacros.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
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