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# View of /trunk/NationalProblemLibrary/Rochester/setSeries9Taylor/S11.10.TaylorPolynomials.PTP02.pg

Wed Apr 25 20:35:08 2012 UTC (12 months, 3 weeks ago) by jj
File size: 1635 byte(s)
Fixed bug 2338, limits needed for function check so that students cannot
enter the original function in place of Taylor polynomials.


    1 ## DESCRIPTION
2 ##   Approximating a Function with a Taylor Series
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Series', 'Taylor', 'Approximate', 'Error')
6 ## Tagged by nhamblet
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Infinite Sequences and Series')
10 ## DBsection('Application of Taylor Polynomials')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19 ## TitleText2('Calculus: Early Transcendentals')
20 ## EditionText2('1')
21 ## AuthorText2('Rogawski')
22 ## Section2('8.4')
23 ## Problem2('1')
24
25 DOCUMENT();        # This should be the first executable line in the problem.
26
28 "PG.pl",
29 "PGbasicmacros.pl",
30 "PGchoicemacros.pl",
32 "PGauxiliaryFunctions.pl"
33 );
34
35 TEXT(beginproblem());
36 $showPartialCorrectAnswers = 1; 37 38 39 TEXT(EV2(<<EOT)); 40 41 (A) Find the fifth degree Taylor polynomial approximation $$T_5(x)$$ centered at $$a = 0$$ to the function $$f(x) = \cos(x).$$$BR
42 $$T_{5}(x) =$$ \{ans_rule(60)\}  $BR$BR
43
44 (B) Find the fifth degree Taylor polynomial approximation $$T_5(x)$$ centered at $$a = 0$$ to the function $$f(x) = \sin(x).$$ $BR 45 $$T_{5}(x) =$$ \{ans_rule(60)\}$BR$BR 46 47 48 (C) Find the fifth degree Taylor polynomial approximation $$T_5(x)$$ centered at $$a = 0$$ to the function $$f(x) = e^x.$$$BR
49 $$T_{5}(x) =$$ \{ans_rule(60)\}  $BR$BR
50
51
52 EOT
53
54 $taylorcos = "1-x^2/2+x^4/24" ; 55$taylorsin = "x - x^3/6 + x^5/120";
56 $taylore = "1 + x + x^2/2 + x^3/6 + x^4/24 + x^5/120"; 57 58 ANS(fun_cmp($taylorcos, limits=>[5,6]));
59 ANS(fun_cmp($taylorsin, limits=>[5,6])); 60 ANS(fun_cmp($taylore, limits=>[5,6]));
61
62 ENDDOCUMENT();