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Sat Sep 8 05:17:01 2007 UTC (5 years, 8 months ago) by sh002i
File size: 3397 byte(s)
Added tags for Rogawski's "Calculus: Early Transcendentals".


    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('calculus', 'derivatives')
6 ## Tagged by YL
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Applications of Differentiation')
10 ## DBsection('How Derivatives Affect the Shape of a Graph')
11 ## Date('')
12 ## Author('')
13 ## Institution('ASU')
14 ## TitleText1('Calculus: Early Transcendentals')
15 ## EditionText1('5')
16 ## AuthorText1('Stewart')
17 ## Section1('4.3')
18 ## Problem1('')
19
20 ## TitleText2('Calculus: Early Transcendentals')
21 ## EditionText2('6')
22 ## AuthorText2('Stewart')
23 ## Section2('4.3')
24 ## Problem2('')
25 ## TitleText3('Calculus: Early Transcendentals')
26 ## EditionText3('1')
27 ## AuthorText3('Rogawski')
28 ## Section3('4.5')
29 ## Problem3('79')
30
31 DOCUMENT();        # This should be the first executable line in the problem.
32
34            "PGbasicmacros.pl",
35            "PGchoicemacros.pl",
37            "PGauxiliaryFunctions.pl",
39
40
41 $a = random(2,7,1); 42$b = random(2,7,1);
43 $c = random(2,7,1); 44 45 TEXT(beginproblem()); 46 47$showPartialCorrectAnswers = 1;
48
49 TEXT(EV2(<<EOT));
50 Suppose that
51 $f(x) = \frac{a x - b}{x + c}.$
52 $BR 53 (A) Find all critical numbers of $$f$$. 54 If there are no critical numbers, enter 'NONE'. 55$BR
56 Critical numbers = \{ans_rule(20)\}
57 $PAR 58 EOT 59 60 ANS(str_cmp('NONE')); 61 62 TEXT(EV2(<<EOT)); 63 (B) Use interval notation to indicate where $$f(x)$$ is increasing. 64$BR
65 $BBOLD Note:$EBOLD  Use 'INF' for $$\infty$$, '-INF' for $$-\infty$$,
66 and use 'U' for the union symbol.
67 $BR 68 Increasing: \{ans_rule(35)\} 69$PAR
70 EOT
71
72 @answers = (interval_cmp("(-Inf,-$c)U(-$c,Inf)"));
74
75 TEXT(EV2(<<EOT));
76 (C) List the $$x$$-coordinates of all local maxima of $$f$$.
77 If there are no local maxima, enter 'NONE'.
78 $BR 79 $$x$$ values of local maxima = \{ans_rule(20)\} 80$PAR
81 EOT
82
83 ANS(str_cmp('NONE'));
84
85 TEXT(EV2(<<EOT));
86 (E) List the $$x$$-coordinates of all local minima of $$f$$.
87 If there are no local minima, enter 'NONE'.
88 $BR 89 $$x$$ values of local minima = \{ans_rule(20)\} 90$PAR
91 EOT
92
93 ANS(str_cmp('NONE'));
94
95 TEXT(EV2(<<EOT));
96 (F) Use interval notation to indicate where $$f(x)$$ is concave up.
97 $BR 98 Concave up: \{ans_rule(25)\} 99$PAR
100 EOT
101
102 @answers = (interval_cmp("(-Inf,-$c)")); 103 ANS(@answers ); 104 105 TEXT(EV2(<<EOT)); 106 (G) Use interval notation to indicate where $$f(x)$$ is concave down. 107$BR
108 Concave down: \{ans_rule(25)\}
109 $PAR 110 EOT 111 112 @answers = (interval_cmp("(-$c,Inf)"));
114
115 TEXT(EV2(<<EOT));
116 (H) List the $$x$$ values of  all inflection points of $$f$$.
117 If there are no inflection points, enter 'NONE'.
118 $BR 119 $$x$$ values of inflection points = \{ans_rule(20)\} 120$PAR
121 EOT
122
123 ANS(str_cmp('NONE'));
124
125 TEXT(EV2(<<EOT));
126 (I) List all horizontal asymptotes of $$f$$.
127  If there are no horizontal asymptotes, enter 'NONE'.
128 $BR 129 Horizontal asymptotes $$y =$$ \{ans_rule(20)\} 130$PAR
131 EOT
132
133 ANS(number_list_cmp( "$a" , strings=>["none"] )); 134 135 TEXT(EV2(<<EOT)); 136 (J) Find all vertical asymptotes of $$f$$. 137 If there are no vertical asymptotes, enter 'NONE'. 138$BR
139 Vertical asymptotes $$x =$$  \{ans_rule(20)\}
140 $PAR 141 EOT 142 143 ANS(number_list_cmp( "-$c" , strings=>["none"] ));
144
145 TEXT(EV2(<<EOT));
146 (K) Use all of the preceding information to sketch a
147 graph of $$f$$.  When you're finished, enter a "1" in the box
148 below.
149 $BR 150 Graph Complete: \{ans_rule(12)\} 151$PAR
152 EOT
153
154 @answers = (num_cmp(1) );
155