Math 1B - Spring 1997 - Ribet - Midterm 2

# Math 1B - Spring 1997 - Ribet - Midterm 2 - Mathematics 1BM...

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Unformatted text preview: Problem Maximum Your Score 1 9 2 14 3 14 4 8 Total 45 At the conclusion of the exam, hand in this exam paper to your TA. 1 Your Name: 1 (9 points) . Solve the initial-value problem y 2 y = 3 e x + 4 , y (0) = 1. 2 Your Name: 2a (8 points) . For which values of x does the series ∞ X n =2 n 3 3 n x n converge? 2b (6 points) . Let f ( x ) be the sum of the series above. Find f (100) (0). 3 Your Name: 3a (7 points) . Decide whether ∞ X n =1 (-1) n tan 1 n 2 converges absolutely, converges condi-tionally, or diverges. 3b (7 points) . Evaluate ∞ X n =0 (-1) n (ln 2) n n ! . 4 Your Name: 4 (8 points) . Find the Maclaurin series for the function 1 √ 1-x 2 . 5...
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