##KEYWORDS('Taylor Series','cos') ##DESCRIPTION ## Taylor Polynomials ##ENDDESCRIPTION ## Shotwell cleaned ## DBsubject('Calculus') ## DBchapter('Infinite Sequences and Series') ## DBsection('Application of Taylor Polynomials') ## Date('6/3/2002') ## Author('') ## Institution('') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('11.12') ## Problem1('16') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PGbasicmacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 0;$d = random(2,6,2) ; BEGIN_TEXT Let $$T_{d}(x)$$ be the Taylor polynomial of degree $$d)\ for the function \( 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? $BR$BR $BITALIC Hint: use the alternating series approximation.$EITALIC $BR$BR Answer: \{ans_rule(20)\} END_TEXT ANS(num_cmp("1/fact(\$d+2)")); ENDDOCUMENT(); # This should be the last executable line in the problem.