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# View of /trunk/NationalProblemLibrary/Rochester/setSeries5IntegralTest/ur_sr_5_13.pg

Sat Nov 17 00:11:09 2007 UTC (5 years, 6 months ago) by jj
File size: 1243 byte(s)
Fixed bug 1390, minor wording changes.  Also cleaned it up a bit.


    1 ## DESCRIPTION
2 ##   Infinite Series with the Integral Test
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Series', 'Converge', 'Diverge', Integral Test')
6 ## Tagged by nhamblet
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Infinite Sequences and Series')
10 ## DBsection('The Integral Test and Estimates of Sums')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
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 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "contextString.pl"
28 );
29
30 TEXT(beginproblem());
31 $showPartialCorrectAnswers = 1; 32 33$a = random(2,9,1);
34 $b = random(2,9,1); 35 36 BEGIN_TEXT 37 Find the value 38 $$\displaystyle \int_1^{\infty} a x^2 e^{-x^3}\;dx =$$ 39 \{ans_rule(20) \}$BR
40 Determine whether the series
41 $$\displaystyle \sum_{n=1}^\infty( a n^2 e^{-n^3} )$$ converges.
42 $BR 43 The seris is 44 \{ pop_up_list(["?", "Convergent", "Divergent"]) \} 45 END_TEXT 46 47 Context("String")->strings->add("Convergent"=>{}, "Divergent"=>{},"?"=>{}); 48 49$ans1 = $a / (8.154845485); 50 ANS(num_cmp("$a/(3*e)"));
51 ANS(String("Convergent")->cmp);
52
53 ENDDOCUMENT();        # This should be the last executable line in the problem.