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# View of /trunk/NationalProblemLibrary/ma123DB/set13/s11_12_17.pg

Wed Oct 11 18:47:47 2006 UTC (6 years, 7 months ago) by ziemer
File size: 1144 byte(s)
changed problem wording. degree of polynomial is not always sixth


    1 ##KEYWORDS('Taylor Series','cos')
2 ##DESCRIPTION
3 ##  Taylor Polynomials
4 ##ENDDESCRIPTION
5
6 ## Shotwell cleaned
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Infinite Sequences and Series')
10 ## DBsection('Application of Taylor Polynomials')
11 ## Date('6/3/2002')
12 ## Author('')
13 ## Institution('')
14 ## TitleText1('Calculus Early Transcendentals')
15 ## EditionText1('4')
16 ## AuthorText1('Stewart')
17 ## Section1('11.12')
18 ## Problem1('16')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23 "PGbasicmacros.pl",
25 "PGauxiliaryFunctions.pl"
26 );
27
28 TEXT(beginproblem());
29 $showPartialCorrectAnswers = 0; 30 31$d = random(2,6,2) ;
32
33 BEGIN_TEXT
34
35 Let $$T_{d}(x)$$ be the Taylor polynomial of degree $$d)\ for the function 36 \( f(x) = \cos(x)$$ at $$a = 0$$. Suppose you approximate $$f(x)$$ by $$T_{d}(x)$$. If $$|x| \leq 1$$, what is the bound for your error of your estimate?
37 $BR$BR
38 $BITALIC Hint: use the alternating series approximation.$EITALIC $BR$BR
39