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# View of /trunk/NationalProblemLibrary/Utah/Calculus_II/set10_Infinite_Series/set10_pr2.pg

Tue Aug 24 14:40:25 2010 UTC (2 years, 9 months ago) by apizer
File size: 1395 byte(s)
Results of running convert_fun_in_dir.sh to clean up problems

    1 #DESCRIPTION
2 #Taylor_series
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 $showPartialCorrectAnswers = 1; 28 29$b = random(2,3,1);
30
31 if ($b==3) { 32$a = random(2,6,1);
33   $c = 3; 34 } else { 35$a = random(3,7,1);
36   $c = random(3,5,2); 37 } 38 39$p = ($c - 1)/2; 40 41 # We'll ask for the m-th derivative, where m=c*b: 42 43$m = $c *$b;
44
45 $endstr='th'; 46 47 # A quick routine to compute m factorial: 48 49$j=0;
50 $mfact=1; 51 while ($j<$m) { 52$j = $j + 1; 53$mfact = $j *$mfact;
54 }
55
57
58 $ans = (-1)**$p * $mfact/($c * $a**$c);
59
60
61 TEXT(EV2(<<EOT));
62
63 Compute the $m$endstr derivative of
64 $f(x) = \arctan\left( \frac{x^{b}}{a} \right)$
65 at $$x=0$$.
66 $BR 67 68 $$\displaystyle f^{(m)}(0) =$$ 69 \{ans_rule(30)\} 70 71$BR
72 $BR 73 Hint: Use the MacLaurin series for $$f(x)$$. 74 75 EOT 76 77 ANS(num_cmp($ans));
78
79
80 ENDDOCUMENT();        # This should be the last executable line in the problem.
81