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

Revision 2937 Revision 2938
38# Let students type "EmptySet" instead of "NONE" 38# Let students type "EmptySet" instead of "NONE"
40Context()->flags->set(noneWord=>"EmptySet"); 40Context()->flags->set(noneWord=>"EmptySet");
41 41
42$a = random(1,5); 42$a = random(1,5);
43$a2 = 2*$a;
43 44
44$ans0 = Compute("$a"); 45$ans0 = Compute("$a");
45$ans1 = Compute("-(1/(2*$a))*(x-$a)^2"); 46$ans1 = Compute("-(1/(2*$a))*(x-$a)^2");
46$ans2 = Compute("-(1/(8*$a^3))*(x-$a)^4"); 47$ans2 = Compute("-(1/(8*$a^3))*(x-$a)^4");
47$ans3 = Compute("-(1/(32*$a^5))*(x-$a)^6"); 48$ans3 = Compute("-(1/(16*$a^5))*(x-$a)^6");
48$ans4 = Compute("-(1/(128*$a^7))*(x-$a)^8"); 49$ans4 = Compute("-(1/(128*$a^6))*(x-$a)^8");
49 50
50Context("Numeric"); 51Context("Numeric");
51$ans5 = Compute("$a"); 52$ans5 = Compute("$a");
52##################################################################### 53#####################################################################
53 54
56Find the first five non-zero terms of Taylor series centered at $$x = a$$ for the function below. 57Find the first five non-zero terms of Taylor series centered at $$x = a$$ for the function below.
57$58\[ 58f(x) = \sqrt{a2 x - x^2} 59f(x) = \sqrt{a2 x - x^2} 59$ 60\]
60$HR 61$HR
61Answer: $$f(x) =$$ \{ans_rule(10)\} $$+$$ \{ans_rule(10)\} $$+$$ \{ans_rule(10)\} $$+$$ \{ans_rule(10)\} $$+$$ \{ans_rule(10)\} $$+ \cdots$$ 62Answer: $$f(x) =$$ \{ans_rule(8)\} $$+$$ \{ans_rule(12)\} $$+$$ \{ans_rule(12)\} $$+$$ \{ans_rule(12)\} $$+$$ \{ans_rule(14)\} $$+ \cdots$$
62$HR 63$HR
63What is the radius of convergence? $BR 64What is the radius of convergence?$BR
64Answer: $$R =$$ \{ans_rule(20)\} 65Answer: $$R =$$ \{ans_rule(10)\}
65\$HR
66END_TEXT 66END_TEXT
67Context()->normalStrings; 67Context()->normalStrings;
68 68
69##################################################################### 69#####################################################################
70 70

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