Math 1B - Spring 1997 - Ribet - Midterm 1

# Math 1B - Spring 1997 - Ribet - Midterm 1 - 1 Your Name...

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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 deﬁne 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. It’s 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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