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

Sun Mar 26 04:58:01 2006 UTC (7 years, 2 months ago) by jj
File size: 1176 byte(s)
Initial import


    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
10 "PG.pl",
11 "PGbasicmacros.pl",
12 "PGchoicemacros.pl",
14 "PGauxiliaryFunctions.pl"
15 );
16
17 # No partial credit on this problem, so we say:
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.