MATH118FS06S

MATH118FS06S - Page 2 of 2 7. The Taylor Polynomial that...

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Math 118 - Final Exam Answeres Spring 2006 Page 1 of 2 1. a) n =0 x n , R = 1 b) dy dx = dy dt dx dt c) f ( x ) = n =0 f ( n ) ( a ) n ! ( x - a ) n d) p > 1 2. a) - e - x 2 + C b) ln ± ± x - 1 x - 2 ± ± + C c) 8 sin - 1 ( x 4 ) + x 2 16 - x 2 + C d) The improper integral diverges. 3. a) b) The slope of the tangent line is -1. 4. a) 1 2 b) Prove by induction the sequence is increasing. Prove that 1 is a lower bound and 3 is an upper bound. The limit is 3. 5. a) This is a geometric series with r = 1 e < 1 hence it converges. b) By the alternating series test, the series converges. c) The sereies converges by the comparison test. d) The series diverges by the n -th term test. 6. The interval of convergence is [ - 3 , 1).
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Math 118 - Final Exam Answeres Spring 2006
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Unformatted text preview: Page 2 of 2 7. The Taylor Polynomial that approximates f ( x ) on [0 , 4] with error less than 0.1 is P 4 ( x ) = 4 X n =0 e n ! 2 n ( x-2) n = e + e 2 ( x-2) + e 8 ( x-2) 2 + e 48 ( x-2) 3 + e 384 ( x-2) 4 8. R 1 / 3 cos( x ) dx 1 3-1 36 = 11 36 with error less than 0.001 since 72 27 &gt; 1000. 9. n =0 n +1 n ! = e 1 + 1 e 1 = 2 e 10. a) y = Ce x 2-1 b) y = 6 x ( x 2 +1) 2 c) 2 D Dy-1 = x + F d) y (0) = e 2 e 2 + e 2 x 2 11. 204 grams of salt....
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MATH118FS06S - Page 2 of 2 7. The Taylor Polynomial that...

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