[rochester] / trunk / rochester_problib / instructiveProblems / NewProblems / benny_ratio2N.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

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Thu Jul 19 16:22:01 2007 UTC (5 years, 10 months ago) by gage
File size: 3264 byte(s)
A collection of problems illustrating how to use MathObjects when
writing WeBWorK questions.


    1 ##DESCRIPTION
2 ##KEYWORDS('series', 'ratio test', 'absolute convergence')
3 ##ENDDESCRIPTION
4
5 DOCUMENT();        # This should be the first executable line in the problem.
6
8 "PGstandard.pl",
9 "PGcourse.pl",
10 "MathObjects.pl",
11 # "source.pl",
12 );
13
14 # No partial credit on this problem, so we say:
16
17 TEXT(beginproblem());
18 $showPartialCorrectAnswers = 0; 19 20 ################### 21 # 22 # Setup 23 24 Context()->variables->add(n => 'Real'); 25 Context()->strings->add(divergent=>{},div=>{alias=>'divergent'}, 26 diverges=>{alias=>'divergent'}); 27 28$a = non_zero_random(-9,9,1);
29 $b = random(1,9,1); 30$c = non_zero_random(-8,8,1);
31
32 $expr_e = Formula("e^(n +$a)");
33 $expr_ne = Formula("e^(n +$a)*sqrt(n + $c)")->reduce; 34$expr_f  = Formula("(n + $b)!")->reduce; 35$expr_nf = Formula("sqrt(n + $c)*(n +$b)!")->reduce;
36
37 $gen = random(0,3,1); 38 39 Context()->texStrings; # Needed here to display the strings below correctly 40 # in the main part of the problem. 41 if ($gen == 0) {
42   $frac = "\frac{$expr_e}{$expr_nf}"; 43$soln1 = Real("0");
44   $soln2 = Real("1"); 45 } 46 47 elsif ($gen == 1) {
48   $frac = "\frac{$expr_ne}{$expr_f}"; 49$soln1 = Real("0");
50   $soln2 = Real("1"); 51 } 52 53 elsif ($gen == 2) {
54   $frac = "\frac{$expr_nf}{$expr_e}"; 55$soln1 = String("infinity");
56   $soln2 = Real("2"); 57 } 58 59 else { 60$frac = "\frac{$expr_f}{$expr_ne}";
61   $soln1 = String("infinity"); 62$soln2 = Real("2");
63   }
64
65 #### Prepare poplist for  question
66 @num_of_sols_pop_up_list = (
67     ' '       => '?',
68        1   => "1. The Ratio Test says that the series converges absolutely.",
69        2   => "2. The Ratio Test says that the series diverges.",
70        3   => "3. The Ratio Test says that the series converges conditionally.",
71        4   => "4. The Ratio Test is inconclusive, but the series converges
72                absolutely by another test or tests.",
73        5   => "5. The Ratio Test is inconclusive, but the series diverges
74                by another test or tests.",
75        6   => "6. The Ratio Test is inconclusive, but the series converges
76                conditionally by another test or tests.",
77 );
78
79 ###################
80 #
81 #  Text
82
83 BEGIN_TEXT
84
85 Consider the series $$NewThing$$
86 $$\displaystyle \sum_{n=1}^{\infty} a_n$$
87 where
88 $a_n = frac$
89 In this problem you must attempt to use the Ratio Test to decide
90 whether the series converges.
91
92 $BR$BR
93
94 Compute
95 $L=\lim_{n\rightarrow\infty} \left| \frac{ a_{n+1} }{a_n} \right|$
96 Enter the numerical value of the limit L if it converges,
97 INF if it diverges to infinity, -INF if it diverges to negative infinity,
98 or DIV if it diverges but not to infinity or negative infinity. $BR 99 $$L =$$ \{ ans_rule( 30) \} 100 101$BR $BR 102 103 Which of the following statements is true?$BR
104 \{pop_up_list(@num_of_sols_pop_up_list)\}
105
106 END_TEXT
107 Context()->normalStrings;
108
109 ###################
110 #
112
113 $checker = sub { 114 115 my ($correct, $student,$ans) = @_;
116
117    Value::Error("Remember to take the absolute value of the limit.")
118       if(($student < 0) ||($student == String("-infinity")));
119
120    ($student ==$correct);
121 };
122
123 ###################
124 #
127 ANS($soln1->cmp(checker=>$checker));