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# View of /trunk/NationalProblemLibrary/Utah/Calculus_II/set10_Infinite_Series/set10_pr10.pg

Tue Aug 24 14:40:25 2010 UTC (2 years, 8 months ago) by apizer
File size: 1257 byte(s)
Results of running convert_fun_in_dir.sh to clean up problems

    1 #DESCRIPTION
2 # Calculation of integrals using power series.
3 #ENDDESCRIPTION
4 ## Author('Utah ww group')
5 ## Institution('Univeristy of Utah')
6 ## DBsubject('Calculus')
7 ## DBchapter('Infinite Sequences and Series')
8 ## DBsection('Taylor and MacLaurin Series')
9 ## AuthorText1('Dale Varberg, Edwin J. Purcell, and Steve E. Rigdon')
10 ## TitleText1('Calculus')
11 ## EditionText1('9')
12 ## Section1('Infinite Series')
13 ## Problem1('')
14 ## KEYWORDS('calculus')
15
16 DOCUMENT();        # This should be the first executable line in the problem.
17
19 "PG.pl",
20 "PGbasicmacros.pl",
21 "PGchoicemacros.pl",
23 "PGauxiliaryFunctions.pl"
24 );
25
26 TEXT(beginproblem());
27 $showPartialCorrectAnswers = 1; 28 29$a = random(0.6,0.8,0.01);
30 $c = random(2,8,1); 31 32 BEGIN_TEXT 33 Assume that $$\sin(x)$$ equals its Maclaurin series for all x.$BR
34 Use the Maclaurin series for $$\sin(c x^2)$$
35 to evaluate the integral
36 $\int_0^{a} \sin(c x^2) \ dx.$
37
38 Your answer will be an infinite series.  Use the first two terms to estimate its value.
39
40 \{ans_rule(40)\}
41 END_TEXT
42
43
44 $soln1 = "$c * x^3 / 3 - $c^3 * x^7 / 42"; 45$soln2 = $c *$a**3 / 3 - $c**3 *$a**7 / 42;
46
47
48 ANS(num_cmp(\$soln2, relTol=>1E-7));
49
50 ENDDOCUMENT();        # This should be the last executable line in the problem.