| … | |
… | |
| 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('13') |
14 | ## Problem1('13') |
|
|
15 | ## TitleText2('Functions Modeling Change'); |
|
|
16 | ## EditionText2('4') |
|
|
17 | ## AuthorText2('Connally') |
|
|
18 | ## Section2('11.5') |
|
|
19 | ## Problem2('13') |
| 15 | ## Author('Adam Spiegler') |
20 | ## Author('Adam Spiegler') |
| 16 | ## Institution('Loyola University Chicago') |
21 | ## Institution('Loyola University Chicago') |
| 17 | |
22 | |
| 18 | DOCUMENT(); |
23 | DOCUMENT(); |
| 19 | |
24 | |
| 20 | loadMacros("PG.pl", |
25 | loadMacros("PG.pl", |
| 21 | "PGbasicmacros.pl", |
26 | "PGbasicmacros.pl", |
| 22 | "PGchoicemacros.pl", |
27 | "PGchoicemacros.pl", |
| 23 | "PGanswermacros.pl", |
28 | "PGanswermacros.pl", |
| 24 | "PGgraphmacros.pl", |
29 | "PGgraphmacros.pl", |
| 25 | "PGauxiliaryFunctions.pl", |
30 | "PGauxiliaryFunctions.pl", |
| 26 | "extraAnswerEvaluators.pl" |
31 | "extraAnswerEvaluators.pl", |
| 27 | ); |
32 | "MathObjects.pl", |
| 28 | |
33 | "PGcourse.pl", |
| 29 | TEXT(beginproblem()); # standard preamble to each problem. |
34 | "AnswerFormatHelp.pl", |
|
|
35 | ); |
|
|
36 | |
|
|
37 | TEXT(beginproblem()); |
|
|
38 | |
|
|
39 | Context("Numeric"); |
| 30 | |
40 | |
| 31 | |
41 | |
| 32 | $showPartialCorrectAnswers = 1; |
42 | $showPartialCorrectAnswers = 1; |
| 33 | |
43 | |
| 34 | $pick = random(0,1,1); |
44 | $pick = random(0,1,1); |
| … | |
… | |
| 60 | |
70 | |
| 61 | for ($i = 0; $i <= 3; $i++){ |
71 | for ($i = 0; $i <= 3; $i++){ |
| 62 | $z[$i] = $q-$d[3-$i]; |
72 | $z[$i] = $q-$d[3-$i]; |
| 63 | $l[$i] = round((-1)**{$pick}*$z[$i]/($z[$i]+$b)**3)}; |
73 | $l[$i] = round((-1)**{$pick}*$z[$i]/($z[$i]+$b)**3)}; |
| 64 | |
74 | |
|
|
75 | Context()->texStrings; |
| 65 | BEGIN_TEXT |
76 | BEGIN_TEXT |
| 66 | Question 13: |
77 | |
| 67 | $BR |
|
|
| 68 | $SPACE |
|
|
| 69 | $BR |
|
|
| 70 | Let \( \displaystyle f(x) = $eqn \) and estimate the one-sided limits below. If you need to enter \( \infty \) or \( - \infty \), enter INFINITY or -INFINITY. |
78 | Let \( \displaystyle f(x) = $eqn \) and estimate the one-sided limits below. If you need to enter \( \infty \) or \( - \infty \), enter INFINITY or -INFINITY. |
| 71 | $BR $SPACE $BR |
79 | $PAR |
| 72 | a) \( \ \displaystyle \lim_{x \to $q^+} f(x) = \) \{ ans_rule(12) \} |
80 | (a) \( \displaystyle \lim_{x \to $q^+} f(x) = \) \{ ans_rule(12) \} |
| 73 | $BR $SPACE $BR |
81 | \{ AnswerFormatHelp("limits") \} |
|
|
82 | $PAR |
| 74 | b) \( \ \displaystyle \lim_{x \to $q^-} f(x) = \) \{ ans_rule(12) \} |
83 | (b) \( \displaystyle \lim_{x \to $q^-} f(x) = \) \{ ans_rule(12) \} |
| 75 | $BR |
84 | \{ AnswerFormatHelp("limits") \} |
|
|
85 | |
| 76 | END_TEXT |
86 | END_TEXT |
|
|
87 | Context()->normalStrings; |
| 77 | |
88 | |
| 78 | ANS(fun_cmp( $right, vars=>['I','N','F','T','Y'] )); |
89 | ANS( Compute($right)->cmp() ); |
| 79 | ANS(fun_cmp( $left, vars=>['I','N','F','T','Y'] )); |
90 | ANS( Compute($left)->cmp() ); |
| 80 | |
91 | |
|
|
92 | Context()->texStrings; |
| 81 | SOLUTION(EV3(<<'END_SOLUTION')); |
93 | SOLUTION(EV3(<<'END_SOLUTION')); |
| 82 | $BR $SPACE $BR |
94 | $PAR |
| 83 | $BBOLD SOLUTION $EBOLD |
95 | $BBOLD SOLUTION $EBOLD |
| 84 | $BR |
96 | $PAR |
| 85 | To find \( \ \displaystyle \lim_{x \to $q^+} f(x) \) we consider what happens to the function when \( x \) is slightly larger than \( $q \). One way to investigate this behavior is to use a table such as the one below: |
97 | To find \( \displaystyle \lim_{x \to $q^+} f(x) \) we consider what happens to the function when \( x \) is slightly larger than \( $q \). One way to investigate this behavior is to use a table such as the one below: |
| 86 | $BR |
98 | $BR |
| 87 | $BCENTER |
99 | $BCENTER |
| 88 | \{ begintable(6) \} |
100 | \{ begintable(6) \} |
| 89 | \{ row ( "\( x \)", "$q", @x ) \} |
101 | \{ row ( "\( x \)", "$q", @x ) \} |
| 90 | \{ row ( "\( f(x) \)", "Undefined", @r ) \} |
102 | \{ row ( "\( f(x) \)", "Undefined", @r ) \} |
| 91 | \{ endtable() \} |
103 | \{ endtable() \} |
| 92 | $ECENTER |
104 | $ECENTER |
| 93 | $BR |
105 | $BR |
| 94 | From the table we can see that \( \ \displaystyle \lim_{x \to $q^+} f(x) = $right_sym \). |
106 | From the table we can see that \( \displaystyle \lim_{x \to $q^+} f(x) = $right_sym \). |
| 95 | $BR $SPACE $BR |
107 | $PAR |
| 96 | |
108 | |
| 97 | To find \( \ \displaystyle \lim_{x \to $q^-} f(x) \) we consider what happens to the function when \( x \) is slightly less than \( $q \). Again we can use a table to investigate this behavior: |
109 | To find \( \displaystyle \lim_{x \to $q^-} f(x) \) we consider what happens to the function when \( x \) is slightly less than \( $q \). Again we can use a table to investigate this behavior: |
| 98 | $BR |
110 | $BR |
| 99 | $BCENTER |
111 | $BCENTER |
| 100 | \{ begintable(6) \} |
112 | \{ begintable(6) \} |
| 101 | \{ row ( "\( x \)", @z , "$q" ) \} |
113 | \{ row ( "\( x \)", @z , "$q" ) \} |
| 102 | \{ row ( "\( f(x) \)", @l, "Undefined" ) \} |
114 | \{ row ( "\( f(x) \)", @l, "Undefined" ) \} |
| 103 | \{ endtable() \} |
115 | \{ endtable() \} |
| 104 | $ECENTER |
116 | $ECENTER |
| 105 | $BR |
117 | $BR |
| 106 | From the table we can see that \( \ \displaystyle \lim_{x \to $q^-} f(x) = $left_sym \). |
118 | From the table we can see that \( \displaystyle \lim_{x \to $q^-} f(x) = $left_sym \). |
| 107 | $BR |
119 | |
| 108 | END_SOLUTION |
120 | END_SOLUTION |
|
|
121 | Context()->normalStrings; |
| 109 | |
122 | |
| 110 | |
123 | |
| 111 | ENDDOCUMENT(); |
124 | ENDDOCUMENT(); |
Parent Directory
| 
Revision Log
| 
Patch