View of /trunk/NationalProblemLibrary/ma123DB/set13/s11_10_44.pg

    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.