View of /trunk/NationalProblemLibrary/Rochester/setSeries5IntegralTest/eva8_3_3.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 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a = random(2,9,1);
   34 $b = random(2,8,1);
   35 $c = $a*$b-$a;
   36 $e = $a + $a -2;
   37 $d = ($e)**($b-1) ;
   38 BEGIN_TEXT
   39 Find the value of
   40 \[ \int_2^{\infty} \frac{dx}{($a x-2)^$b} \] $BR
   41 \{ans_rule(20)\} $BR
   42 Determine whether $BR
   43 \[ \sum_{n=2}^\infty \frac{1}{($a n-2)^$b} \] $BR
   44 is a convergent series. Enter C if series is convergent, D if series is divergent.
   45 \{ans_rule(1)\} $BR
   46 
   47 END_TEXT
   48 
   49 $ans1 = 1/($c*$d);
   50 $ans2 = "C" ;
   51 ANS(num_cmp($ans1));
   52 ANS(str_cmp($ans2));
   53 
   54 ENDDOCUMENT();        # This should be the last executable line in the problem.