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

    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 
   22 loadMacros(
   23 "PGbasicmacros.pl",
   24 "PGanswermacros.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 
   40 Answer:  \{ans_rule(20)\}
   41 
   42 END_TEXT
   43 
   44 
   45 
   46 ANS(num_cmp("1/fact($d+2)"));
   47 
   48 ENDDOCUMENT();        # This should be the last executable line in the problem.