final fall06

# Thomas' Calculus: Early Transcendentals

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Mathematics 104 Fall Term 2006 Final Examination January 18, 2007 1. Evaluate Z sin(ln t ) dt . 2. Evaluate Z dx 9 x 2 + 16 . 3. a) Does the following series converge or diverge? Give your reasons. X n =1 ln n + sin n n 3 / 2 . b) Does the following integral converge or diverge? Give your reasons. Z 0 sin x x 2 dx . 4. Approximate the following integral with an error less than 10 - 3 . Show your work. Z 1 / 10 0 cos t dt . 5. Find lim x 0 x cos x - xe - x 2 sin 3 x . 6. Find all solutions, in Cartesian form ( a + ib ), of z 4 + 8 iz = 0. 7. The region bounded by the curve
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Unformatted text preview: y = x 3 + 1, the line x = 0, and the line y = 9 is revolved around the line x = 3. Find the volume. 8. Find the length of the curve given in parametric form by x = sin-1 t , y = ln √ 1-t 2 for 0 ≤ t ≤ 1 2 . 9. Find all real solutions to the diﬀerential equation x dy dx + 2 y = sin x . 10. Find all real solutions to the diﬀerential equation y 00-4 y + 8 y = 16 x 2 ....
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## This homework help was uploaded on 02/12/2008 for the course MATH 104 taught by Professor Nelson during the Fall '07 term at Princeton.

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