View of /trunk/NationalProblemLibrary/Rochester/setSeries5IntegralTest/eva8_3_1.pg

    1 #DESCRIPTION
    2 # Series.  Integral Test
    3 #ENDDESCRIPTION
    4 
    5 #KEYWORDS('Series' , 'Integral Test' )
    6 
    7 DOCUMENT();        # This should be the first executable line in the problem.
    8 
    9 loadMacros(
   10 "PG.pl",
   11 "PGbasicmacros.pl",
   12 "PGchoicemacros.pl",
   13 "PGanswermacros.pl",
   14 "PGauxiliaryFunctions.pl"
   15 );
   16 
   17 # No partial credit on this problem, so we say:
   18 install_problem_grader(~~&std_problem_grader);
   19 
   20 
   21 TEXT(beginproblem());
   22 $showPartialCorrectAnswers = 0;
   23 
   24 
   25 $a = random(2,9,1);
   26 $p = random(2,8,1);
   27 
   28 BEGIN_TEXT
   29 Compute the value of the following improper integral if it
   30 converges.  If it diverges, enter INF if it diverges to infinity,
   31 MINF if it diverges to minus infinity, or DIV otherwise (hint:
   32 integrate by parts).
   33 
   34 \[ \int_1^{\infty} \frac{$a \ln(x)}{x^$p} dx\] $BR
   35 \{ans_rule(20)\} $BR
   36 Determine whether $BR
   37 \( \displaystyle \sum_{n=1}^\infty( \frac{$a \ln(n)}{n^$p} ) \) $BR
   38 is a convergent series.
   39 Enter C if the series is convergent, or D if it is divergent.
   40 \{ans_rule(1)\} $BR
   41 
   42 END_TEXT
   43 
   44 $ans1 = $a/(1-$p)**2 ;
   45 $ans2 = "C" ;
   46 
   47 ANS(num_cmp($ans1, strings=>['INF', 'MINF', 'DIV']));
   48 ANS(str_cmp($ans2));
   49 
   50 ENDDOCUMENT();        # This should be the last executable line in the problem.