Practice Exam 2b

Practice Exam 2b - (a) X n =0 2 n + 3 n-1 5 n (b) X n =1 n...

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Mathematics 115b Mid-term # 2 4/8/08 Name: Section: Please answer all SIX questions; each question is worth TEN points. You may use the table of integrals supplied with the test. However, books, notes, calculators, computers, cellphones may NOT be used. 1 2 3 4 5 6 Total (1) Sketch the curve with polar equation r = 1 + cos 3 θ , and find the area that it encloses.
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(2) (a) Sketch the curve x = 4 - ( t - 1) 2 , y = t ( t - 1)( t - 2) , 0 < t < 2. (b) Indicate with an arrow the direction in which the curve is traced as t increases. (c) Find the points where the curve has horizontal tangents and where it has vertical tangents.
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(3) For each series, either evaluate the sum or explain why the series is divergent.
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Unformatted text preview: (a) X n =0 2 n + 3 n-1 5 n (b) X n =1 n sin(1 /n ) (4) Is the series X n =1 3 n-2 5 n 2 + 7 n + 13 convergent or divergent? Give reasons. (5) Are the following series absolutely convergent, conditionally convergent or divergent? Give reasons. (a) X n =1 (-1) n n 2 / 3 (b) X n =1 (-1) n n 3 / 2 (6) Find the radius of convergence and interval of convergence of the series (a) X n =1 ( x-1) n n 2 2 n (b) X n =1 ( n !) 2 x n (2 n )!...
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This note was uploaded on 01/11/2010 for the course MATH 115 at Yale.

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Practice Exam 2b - (a) X n =0 2 n + 3 n-1 5 n (b) X n =1 n...

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