Math 1B - Spring 1997 - Ribet - Midterm 2

Math 1B - Spring 1997 - Ribet - Midterm 2 - Problem Maximum...

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Mathematics 1BM Professor K. A. Ribet Second Midterm Exam April 9, 1997 60 Evans and 2060 VLSB 9:10–10 AM Your Name: TA: This booklet comprises a cover sheet and four pages of questions. Please check that your booklet is complete; write your name on this cover sheet and the four question sheets. As you turn through the pages, look for the easy questions — do them first. Remember that this exam is only 50 minutes long! You need not simplify your answers unless you are specifically asked to do so. It is essential to write legibly and show your work . If your work is absent or illegible, and your answer is not perfectly correct, then no partial credit can be awarded. Completely correct answers which are given without justification may receive little or no credit. During this exam, you are not allowed to use calculators or consult your notes or books.
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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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