[npl] / trunk / NationalProblemLibrary / LoyolaChicago / Precalc / Chap9Sec5 / Q15.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# Diff of /trunk/NationalProblemLibrary/LoyolaChicago/Precalc/Chap9Sec5/Q15.pg

Revision 2460 Revision 2461
10## TitleText1('Functions Modeling Change') 10## TitleText1('Functions Modeling Change')
11## EditionText1('3') 11## EditionText1('3')
12## AuthorText1('Connally') 12## AuthorText1('Connally')
13## Section1('9.5) 13## Section1('9.5)
14## Problem1('15') 14## Problem1('15')
15## TitleText2('Functions Modeling Change');
16## EditionText2('4')
17## AuthorText2('Connally')
18## Section2('11.5')
19## Problem2('18')
16## Institution('Loyola University Chicago') 21## Institution('Loyola University Chicago')
17 22
18DOCUMENT(); 23DOCUMENT();
19 24
21 "PGbasicmacros.pl", 26 "PGbasicmacros.pl",
22 "PGchoicemacros.pl", 27 "PGchoicemacros.pl",
24 "PGgraphmacros.pl", 29 "PGgraphmacros.pl",
25 "PGauxiliaryFunctions.pl", 30 "PGauxiliaryFunctions.pl",
27 ); 32 "MathObjects.pl",
28 33 "PGcourse.pl",
29TEXT(beginproblem()); # standard preamble to each problem. 34 "AnswerFormatHelp.pl",
35);
36
37TEXT(beginproblem());
38
39Context("Numeric");
30 40
31 41
32$showPartialCorrectAnswers = 1; 42$showPartialCorrectAnswers = 1;
33 43
34$h = non_zero_random(1,7,1); 44$h = non_zero_random(1,7,1);
35$k = non_zero_random(1,7,1); 45$k = non_zero_random(1,7,1);
36$p = random(2,3,1); 46$p = random(2,3,1);
37 47
38if ($p == 2){ 48if ($p == 2){
39 $f[0] = "1/(x-4)^2+2 for x in <-1,3.99> using color:blue and weight:2"; 49$f[0] = "1/(x-4)^2+2 for x in <-1,3.99> using color:blue and weight:2";
40 $f[1] = "1/(x-4)^2+2 for x in <4.01,9> using color:blue and weight:2"; 50$f[1] = "1/(x-4)^2+2 for x in <4.01,9> using color:blue and weight:2";
41 $ymax = 10;$ymin = -1; valign = 'top';yst = 1.9; 51 $ymax = 10;$ymin = -1; valign = 'top';yst = 1.9;
42 $left = "INFINITY";$left_sym = "\infty"} 52 $left = "INFINITY";$left_sym = "\infty"}
43else { 53else {
51$graph->lb('reset'); 61$graph->lb('reset');
52$graph->lb(new Label(4,-0.1,$h,'red','right','top')); 62$graph->lb(new Label(4,-0.1,$h,'red','right','top'));
53$graph->lb(new Label(-.15,$yst,"$k",'green','right',$valign)); 63$graph->lb(new Label(-.15,$yst,"$k",'green','right',$valign));
54$graph->lb(new Label(8.7,-.05,"x",'black','left','bottom')); 64$graph->lb(new Label(8.7,-.05,"x",'black','left','bottom'));
55$graph->lb(new Label(-.05,$ymax-.1,"y",'black','right','top')); 65$graph->lb(new Label(-.05,$ymax-.1,"y",'black','right','top'));
56$graph->moveTo(4,$ymin); 66$graph->moveTo(4,$ymin);
57$graph->lineTo(4,$ymax,'red'); 67$graph->lineTo(4,$ymax,'red');
58$graph->moveTo(-1,2); 68$graph->moveTo(-1,2);
59$graph->lineTo(9,2,'green'); 69$graph->lineTo(9,2,'green');
60plot_functions( $graph,$f[0],$f[1] ); 70plot_functions($graph, $f[0],$f[1] );
61$fig = image(insertGraph($graph), width => 300, height => 300, tex_size => 500); 71$fig = image(insertGraph($graph), width => 300, height => 300, tex_size => 500);
62 72
63$right = "INFINITY"; 73$right = "INFINITY";
64$pos = "$k"; 74$pos = "$k";
65$neg = "$k"; 75$neg = "$k";
66 76
67 77
78Context()->texStrings;
68BEGIN_TEXT 79BEGIN_TEXT
69Question 15: 80
70$BR 71$SPACE
72$BR 73Using the graph of the rational function $$y = f(x)$$ given in the figure below, evaluate the limits. If you need to enter $$\infty$$ or $$- \infty$$, type INFINITY or -INFINITY. 81Using the graph of the rational function $$y = f(x)$$ given in the figure below, evaluate the limits. If you need to enter $$\infty$$ or $$- \infty$$, type INFINITY or -INFINITY. 74$BR $SPACE$BR 82$PAR 75$BCENTER 83$BCENTER 76$fig 84$fig 77$ECENTER 85$ECENTER 78$BR 86$BR 79a)$SPACE $$\displaystyle \lim_{x \to \infty} f(x) =$$ \{ ans_rule(10) \} 87(a) $$\displaystyle \lim_{x \to \infty} f(x) =$$ \{ ans_rule(10) \}
80$BR$SPACE $BR 88\{ AnswerFormatHelp("limits") \} 89$PAR
81b) $SPACE $$\displaystyle \lim_{x \to - \infty} f(x) =$$ \{ ans_rule(10) \} 90(b) $$\displaystyle \lim_{x \to - \infty} f(x) =$$ \{ ans_rule(10) \} 82$BR $SPACE$BR 91\{ AnswerFormatHelp("limits") \}
92$PAR 83c)$SPACE $$\displaystyle \lim_{x \to h^+} f(x) =$$ \{ ans_rule(10) \} 93(c) $$\displaystyle \lim_{x \to h^+} f(x) =$$ \{ ans_rule(10) \}
84$BR$SPACE $BR 94\{ AnswerFormatHelp("limits") \} 95$PAR
85d) $SPACE $$\displaystyle \lim_{x \to h^-} f(x) =$$ \{ ans_rule(10) \} 96(d) $$\displaystyle \lim_{x \to h^-} f(x) =$$ \{ ans_rule(10) \} 97\{ AnswerFormatHelp("limits") \} 86$BR 98$BR 87END_TEXT 99END_TEXT 100Context()->normalStrings; 88 101 89ANS(fun_cmp($pos, vars=>['I','N','F','T','Y']) ); 102ANS( Compute($pos)->cmp() ); 90ANS(fun_cmp($neg, vars=>['I','N','F','T','Y']) ); 103ANS( Compute($neg)->cmp() ); 91ANS(fun_cmp($right, vars=>['I','N','F','T','Y']) ); 104ANS( Compute($right)->cmp() ); 92ANS(fun_cmp($left, vars=>['I','N','F','T','Y']) ); 105ANS( Compute($left)->cmp() ); 93 106 107Context()->texStrings; 94SOLUTION(EV3(<<'END_SOLUTION')); 108SOLUTION(EV3(<<'END_SOLUTION')); 95$BR $SPACE$BR 109$PAR 96$BBOLD SOLUTION $EBOLD 110$BBOLD SOLUTION $EBOLD 97$BR 111$PAR 98There is a horizontal asymptote at $$y = k$$, so 112There is a horizontal asymptote at $$y = k$$, so 99$$\displaystyle \lim_{x \to \infty} f(x) = k \ \ \$$ and $$\ \ \ \displaystyle \lim_{x \to - \infty} f(x) = k$$. 113$$\displaystyle \lim_{x \to \infty} f(x) = k$$ and $$\displaystyle \lim_{x \to - \infty} f(x) = k$$. 100$BR $SPACE$BR 114$PAR 101There is a vertical asymptote at $$x = h$$ such that 115There is a vertical asymptote at $$x = h$$ such that 102$$\displaystyle \lim_{x \to h^+} f(x) = \infty \ \ \$$ and $$\ \ \ \displaystyle \lim_{x \to h^-} f(x) = left_sym$$. 116$$\displaystyle \lim_{x \to h^+} f(x) = \infty$$ and $$\displaystyle \lim_{x \to h^-} f(x) = left_sym$$. 103$BR 117
104END_SOLUTION 118END_SOLUTION
119Context()->normalStrings;
105 120
106 121
107ENDDOCUMENT(); 122ENDDOCUMENT();

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