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

    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 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.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.