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# View of /trunk/NationalProblemLibrary/Utah/Calculus_II/set10_Infinite_Series/set10_pr13.pg

Tue Aug 24 14:40:25 2010 UTC (2 years, 8 months ago) by apizer
File size: 1375 byte(s)
Results of running convert_fun_in_dir.sh to clean up problems

1 #DESCRIPTION
2 #  Taylor_Polynomials
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 $showPartialCorrectAnswers = 0; 28 29$a = 1 ;
30 $b = random(3,7,2) ; 31$d = 1 ;
32
33 # a simple code to perform a calculation.
34   $i = 1; 35$f = 1;
36
37   while ($i <=$b ) {
38               $f =$f*$i ; 39$i = $i + 1; 40 } 41 42 TEXT(EV2(<<EOT)); 43 44 Let $$T_{k}(x)$$: be the Taylor polynomial of degree k of the function 45 $$f(x) = \sin(x)$$ 46 at $$a = 0$$.$BR
47
48 Suppose you approximate $$f(x)$$ by $$T_{k}(x)$$, and if $$|x| \leq 1$$, how many terms
49 do you need (that is, what is k) for you to have your error to be less than
50 $$\frac{1}{f}$$ ?
51 (Hint: use the alternating series approximation.)
52
53 $BR 54 55 \{ans_rule(20)\} 56 57 EOT 58 59$answer = $b - 2; 60 ANS(num_cmp($answer));
61
62 ENDDOCUMENT();        # This should be the last executable line in the problem.
63