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Fri Jun 18 12:54:22 2010 UTC (2 years, 11 months ago) by gage
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1 ## DESCRIPTION
2 ##   Evaluate Limits at a Vertical Asymptote
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Limit', 'Infinity', 'Vertical Asymptote', 'One-Sided')
6 ## Tagged by nhamblet
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Limits and Derivatives')
10 ## DBsection('The Limit of a Function')
11 ## Date('12/29/08')
12 ## Author('N. Srivastava')
13 ## Institution('Union College')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23   "PGstandard.pl",
24   "PGunion.pl",            # Union College utilities
25   "MathObjects.pl",
26   "alignedChoice.pl",      # for aligned answer blanks
27   "PGcourse.pl",           # Customization file for the course
28 );
29
30 TEXT(beginproblem());
31
32 ###################################
33 # Setup
34
35 Context("Numeric")->flags->set(reduceConstants => 0);
36
37 $a1 = random(1,5,1); 38$a  = 2 * $a1; 39$s  = random(-1,1,2);
40 $b1 = random(10,40,1); 41$b  = $s *$b1;
42 $c1 = random(1,5,1); 43$c  = 1+2*$c1; 44 45 if ($s == 1) {
46   $ans1 = -(Infinity); 47$ans2 = Infinity;
48 } else {
49   $ans1 = Infinity; 50$ans2 = -(Infinity);
51 }
52
53 $f = Formula("$b x");
54 $g = Formula("$c - $a x"); 55$f_over_g = ($f/$g)->reduce;
56
57 $C = Formula("$c/a"); 58 59 ################################### 60 # Use an alignment to present the questions and answer rules 61 ################################### 62 63 Context()->texStrings; 64alignment = new_aligned_list(
65    equals => 1, ans_rule_len => 20, numbered => 1,
66    row_spacing => 5, tex_spacing => "5pt"
67 );
68 alignment->qa( 69 "$$\displaystyle\lim_{x\to{(C)}^+} f_over_g$$",ans1->cmp,
70  "$$\displaystyle\lim_{x\to{(C)}^-} f_over_g$$", $ans2->cmp, 71 ); 72 Context()->normalStrings; 73 74 ################################### 75 # Main text 76 77 BEGIN_TEXT 78 Evaluate the following limits: 79 \{$alignment->print_q\}
80 $INFINITY_MESSAGE 81 END_TEXT 82 83 ################################### 84 # Answer checking 85 86$showPartialCorrectAnswers = 0;
87 ANS(\$alignment->correct_ans);
88
89
90 COMMENT('MathObject version');
91 ENDDOCUMENT();