[npl] / trunk / NationalProblemLibrary / LoyolaChicago / Precalc / Chap9Sec5 / Q13.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# Diff of /trunk/NationalProblemLibrary/LoyolaChicago/Precalc/Chap9Sec5/Q13.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('13') 14## Problem1('13')
15## TitleText2('Functions Modeling Change');
16## EditionText2('4')
17## AuthorText2('Connally')
18## Section2('11.5')
19## Problem2('13')
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$pick = random(0,1,1); 44$pick = random(0,1,1);
60 70
61for ($i = 0;$i <= 3; $i++){ 71for ($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
75Context()->texStrings;
65BEGIN_TEXT 76BEGIN_TEXT
66Question 13: 77
67$BR 68$SPACE
69$BR 70Let $$\displaystyle f(x) = eqn$$ and estimate the one-sided limits below. If you need to enter $$\infty$$ or $$- \infty$$, enter INFINITY or -INFINITY. 78Let $$\displaystyle f(x) = eqn$$ 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 72a) $$\ \displaystyle \lim_{x \to q^+} f(x) =$$ \{ ans_rule(12) \} 80(a) $$\displaystyle \lim_{x \to q^+} f(x) =$$ \{ ans_rule(12) \} 73$BR $SPACE$BR 81\{ AnswerFormatHelp("limits") \}
82$PAR 74b) $$\ \displaystyle \lim_{x \to q^-} f(x) =$$ \{ ans_rule(12) \} 83(b) $$\displaystyle \lim_{x \to q^-} f(x) =$$ \{ ans_rule(12) \} 75$BR 84\{ AnswerFormatHelp("limits") \}
85
76END_TEXT 86END_TEXT
87Context()->normalStrings;
77 88
78ANS(fun_cmp( $right, vars=>['I','N','F','T','Y'] )); 89ANS( Compute($right)->cmp() );
79ANS(fun_cmp( $left, vars=>['I','N','F','T','Y'] )); 90ANS( Compute($left)->cmp() );
80 91
92Context()->texStrings;
81SOLUTION(EV3(<<'END_SOLUTION')); 93SOLUTION(EV3(<<'END_SOLUTION'));
82$BR$SPACE $BR 94$PAR
83$BBOLD SOLUTION$EBOLD 95$BBOLD SOLUTION$EBOLD
84$BR 96$PAR
85To 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: 97To 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
94From the table we can see that $$\ \displaystyle \lim_{x \to q^+} f(x) = right_sym$$. 106From the table we can see that $$\displaystyle \lim_{x \to q^+} f(x) = right_sym$$.
95$BR$SPACE $BR 107$PAR
96 108
97To 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: 109To 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
106From the table we can see that $$\ \displaystyle \lim_{x \to q^-} f(x) = left_sym$$. 118From the table we can see that $$\displaystyle \lim_{x \to q^-} f(x) = left_sym$$.
107\$BR 119
108END_SOLUTION 120END_SOLUTION
121Context()->normalStrings;
109 122
110 123
111ENDDOCUMENT(); 124ENDDOCUMENT();

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