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# View of /trunk/NationalProblemLibrary/UMN/calculusStewartCCC/s_11_10_prob02.pg

Mon Apr 23 18:50:03 2012 UTC (13 months ago) by jj
File size: 2296 byte(s)
Fixed bug 2331, and corrected some wrong answers.


    1 #DESCRIPTION
2 ##  Calculus: Taylor and Maclaurin series
3 ##ENDDESCRIPTION
4
5 ##KEYWORDS('calculus', 'series', taylor series', 'maclaurin series')
6
7 ## DBsubject('Calculus')
8 ## DBchapter('Infinite Sequences and Series')
9 ## DBsection('Taylor and Maclaurin Series')
10 ## Date('04/26/2010')
11 ## Author('Justin Sukiennik')
12 ## Institution('University of Minnesota')
13 ## TitleText1('Calculus: Concepts and Contexts')
14 ## EditionText1('4 Custom UMTYMP Ed.')
15 ## AuthorText1('Stewart')
16 ## Section1('11.10')
17 ## Problem1('')
18
19 #####################################################################
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23   "PGstandard.pl",
24   "MathObjects.pl",
26   "PGcourse.pl",
27 );
28
29 #####################################################################
31
32 $showPartialCorrectAnswers = 0; 33 34 TEXT(beginproblem()); 35 36 ##################################################################### 37 Context("Numeric"); 38 # Let students type "EmptySet" instead of "NONE" 39 Context()->constants->add(EmptySet => Set()); 40 Context()->flags->set(noneWord=>"EmptySet"); 41 42$a = random(1,5);
43 $a2 = 2*$a;
44
45 $ans0 = Compute("$a");
46 $ans1 = Compute("-(1/(2*$a))*(x-$a)^2"); 47$ans2 = Compute("-(1/(8*$a^3))*(x-$a)^4");
48 $ans3 = Compute("-(1/(16*$a^5))*(x-$a)^6"); 49$ans4 = Compute("-(1/(128*$a^6))*(x-$a)^8");
50
51 Context("Numeric");
52 $ans5 = Compute("$a");
53 #####################################################################
54
55 Context()->texStrings;
56 BEGIN_TEXT
57 Find the first five non-zero terms of Taylor series centered at $$x = a$$ for the function below.
58 $59 f(x) = \sqrt{a2 x - x^2} 60$
61 $HR 62 Answer: $$f(x) =$$ \{ans_rule(8)\} $$+$$ \{ans_rule(12)\} $$+$$ \{ans_rule(12)\} $$+$$ \{ans_rule(12)\} $$+$$ \{ans_rule(14)\} $$+ \cdots$$ 63$HR
64 What is the radius of convergence? $BR 65 Answer: $$R =$$ \{ans_rule(10)\} 66 END_TEXT 67 Context()->normalStrings; 68 69 ##################################################################### 70 71 WEIGHTED_ANS( ($ans0)->cmp(), 10 );
72 WEIGHTED_ANS( ($ans1)->cmp(), 10 ); 73 WEIGHTED_ANS( ($ans2)->cmp(), 10 );
74 WEIGHTED_ANS( ($ans3)->cmp(), 10 ); 75 WEIGHTED_ANS( ($ans4)->cmp(), 10 );
76 Context("Numeric");
77 WEIGHTED_ANS( (\$ans5)->cmp(), 50 );
78
79 ENDDOCUMENT();        # This should be the last executable line in the problem.


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