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Fri Oct 7 16:42:13 2011 UTC (19 months, 2 weeks ago) by glarose
File size: 3287 byte(s)
LoyolaChicago 9.5: 4e tagging, updates.

    1 # DESCRIPTION
2 # Problem from Functions Modeling Change, Connally et al., 3rd ed.
3 # WeBWorK problem written by Adam Spiegler, <aspiegler@luc.edu>
4 # ENDDESCRIPTION
5
6 ## DBsubject('Precalculus')
7 ## DBchapter('Polynomial And Rational Functions')
8 ## DBsection('The Short-Run Behavior Of Rational Functions')
9 ## KEYWORDS('rational','fraction','polynomial,'asymptote','intercept')
10 ## TitleText1('Functions Modeling Change')
11 ## EditionText1('3')
12 ## AuthorText1('Connally')
13 ## Section1('9.5)
14 ## Problem1('14')
15 ## TitleText2('Functions Modeling Change');
16 ## EditionText2('4')
17 ## AuthorText2('Connally')
18 ## Section2('11.5')
19 ## Problem2('14')
20 ## Author('Adam Spiegler and Paul Pearson')
21 ## Institution('Loyola University Chicago and Fort Lewis College')
22
23 DOCUMENT();
24
26            "PGbasicmacros.pl",
27 #           "PGchoicemacros.pl",
29 #           "PGgraphmacros.pl",
30            "PGauxiliaryFunctions.pl",
32 "MathObjects.pl",
34 "PGcourse.pl",
35            );
36
37 TEXT(beginproblem());
38
39 Context("Numeric");
40
41 $showPartialCorrectAnswers = 1; 42 43$pick = random(0,1,1);
44 $k = non_zero_random(1,9,2); 45$b = non_zero_random(2,10,2);
46
47 $eqn = "\frac{$k-x}{(x-$b)^2}"; 48 49 if ($k > $b) { 50$right = "INFINITY";
51    $right_sym = "\infty"; 52$left = "INFINITY";
53    $left_sym = "\infty"} 54 else { 55$right = "-INFINITY";
56    $left = "-INFINITY"; 57$right_sym = "- \infty";
58    $left_sym = "- \infty"}; 59 60 61$d[0] = .001;
62 $d[1] = .01; 63$d[2] = .1;
64 $d[3] = 1; 65 66 for ($i = 0; $i <= 3;$i++){
67   $x[$i] = $b+$d[$i]; 68$r[$i] = round(($k-$x[$i])/($x[$i]-$b)**2)}; 69 70 for ($i = 0; $i <= 3;$i++){
71   $z[$i] = $b-$d[3-$i]; 72$l[$i] = round(($k-$z[$i])/($z[$i]-$b)**2)}; 73 74 Context()->texStrings; 75 BEGIN_TEXT 76 Estimate the one-sided limits below. 77$PAR
78 (a) As $$x \to b^+$$,  $$\displaystyle eqn \to$$ \{ ans_rule(12) \}
80 $PAR 81 (b) As $$x \to b^-$$, $$\displaystyle eqn \to$$ \{ ans_rule(12) \} 82 \{ AnswerFormatHelp("limits") \} 83 END_TEXT 84 Context()->normalStrings; 85 86 ANS( Compute("$right")->cmp() );
87 ANS( Compute("$left")->cmp() ); 88 89 #ANS(fun_cmp($right, vars=>['I','N','F','T','Y']  ));
90 #ANS(fun_cmp( $left, vars=>['I','N','F','T','Y'] )); 91 92 Context()->texStrings; 93 SOLUTION(EV3(<<'END_SOLUTION')); 94$PAR
95 $BBOLD SOLUTION$EBOLD
96 $PAR 97 (a) 98 To find $$\displaystyle \lim_{x \to b^+} f(x)$$ we consider what happens to the function when $$x$$ is slightly larger than $$b$$. One way to investigate this behavior is to use a table such as the one below: 99$BR
100 $BCENTER 101 \{ begintable(6) \} 102 \{ row ( "$$x$$", "$b", @x ) \}
103 \{ row ( "$$f(x)$$", "Undefined", @r ) \}
104 \{ endtable() \}
105 $ECENTER 106$BR
107 From the table we can see that $$\displaystyle \lim_{x \to b^+} f(x) = right_sym$$.
108 $PAR 109 (b) 110 To find $$\displaystyle \lim_{x \to b^-} f(x)$$ we consider what happens to the function when $$x$$ is slightly less than $$b$$. Again we can use a table to investigate this behavior: 111$BR
112 $BCENTER 113 \{ begintable(6) \} 114 \{ row ( "$$x$$", @z , "$b" ) \}
115 \{ row ( "$$f(x)$$", @l, "Undefined" ) \}
116 \{ endtable() \}
117 $ECENTER 118$BR
119 From the table we can see that $$\displaystyle \lim_{x \to b^-} f(x) = left_sym$$.
120
121 END_SOLUTION
122 Context()->normalStrings;
123
124 COMMENT('MathObject version');
125 ENDDOCUMENT();