Math 1B - Spring 1997 - Ribet - Midterm 1

Math 1B - Spring 1997 - Ribet - Midterm 1 - 1 Your Name: 1a...

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Mathematics 1BM Professor K. A. Ribet First Midterm Exam February 26, 1997 60 Evans and 2060 VLSB 9:10–10 AM Your Name: TA: This booklet should consist of a cover sheet, four pages of questions, and a final reference page of formulas. Please check that your booklet is complete, and 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. Problem Maximum Your Score 1 11 2 12 3 13 4 9 Total 45 At the conclusion of the exam, hand in this exam paper to your TA.
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Unformatted text preview: 1 Your Name: 1a (5 points) . Write the repeating decimal 0 . 461538 as a quotient of two integers. 1b (6 points) . Evaluate Z 1-1 dx | x | 5 / 6 . 2 Your Name: 2a (5 points) . Find Z dx x 1 / 2 + x 3 / 2 . 2b (7 points) . Compute Z x 2 e-x dx . 3 Your Name: 3a (6 points) . Find any two of the constants A , B , C , D : x 3 + 2 x 2-3 x-5 ( x 2 + 3 x + 2) 2 = A ( x + 1) 2 + B x + 1 + C ( x + 2) 2 + D x + 2 . 3b (7 points) . The curve y = x (0 x 1) is rotated about the x-axis. Find the area of the resulting surface. 4 Your Name: 4 (9 points) . Let c 1 = 1, and dene c n +1 = 1 + 1 c n for all n 1. Thus c 2 = 2, c 3 = 3 2 , c 4 = 5 3 , ... . a. Is the sequence { c n } bounded? Is it monotonic? Explain. b. Its a fact that there is a number L 1 . 61803 such that c n L as n . Using the equation c n +1 = 1 + 1 c n , show that L 2-L-1 = 0. 5...
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Math 1B - Spring 1997 - Ribet - Midterm 1 - 1 Your Name: 1a...

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