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    1 ##KEYWORDS('Taylor Series' , 'Integrals' )
2 ##DESCRIPTION
3 ## Calculation of integrals using power series.
4 ##ENDDESCRIPTION
5
6 ## Shotwell cleaned
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Infinite Sequences and Series')
10 ## DBsection('Taylor and Maclaurin Series')
11 ## Date('6/3/2002')
12 ## Author('')
13 ## Institution('')
14 ## TitleText1('Calculus Early Transcendentals')
15 ## EditionText1('4')
16 ## AuthorText1('Stewart')
17 ## Section1('11.10')
18 ## Problem1('44')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
22 loadMacros(
23 "PGbasicmacros.pl",
24 "PGanswermacros.pl",
25 "PGauxiliaryFunctions.pl"
26 );
27
28 TEXT(beginproblem());
29 $showPartialCorrectAnswers = 1; 30 31$a = random(0.1,0.2,0.01);
32 $b = non_zero_random(2,5,1); 33 34 BEGIN_TEXT 35 Let $$F(x) = \int_0^{x} e^{-b t^4} \ dt$$.$BR$BR 36 Find the MacLaurin polynomial of degree 5 for $$F(x)$$.$BR$BR 37 Answer: \{ans_rule(50)\}$BR$BR 38 39 Use this polynomial to estimate the value of 40 $$\int_0^{a} e^{-b x^4} \ dx$$.$BR$BR 41 Answer: \{ans_rule(40)\} 42 END_TEXT 43 44 45$soln1 = "x - $b * x^5 / 5"; 46$soln2 = "$a -$b * $a^5 / 5"; 47 48 49 ANS(fun_cmp($soln1));
50 ANS(num_cmp(\$soln2,relTol=>1E-7));
51
52
53 ENDDOCUMENT();        # This should be the last executable line in the problem.


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