Winter 2006 - Reynold's Class - Quiz 4 (Version A)

Winter 2006 - Reynold's Class - Quiz 4 (Version A) - Math...

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Unformatted text preview: Math 20D, Lecture C, Winter 2006 24 February 2006 Quiz 4, version A Name: ID #: Section Time: Show all work clearly and in order, and circle your final answers. You have 20 minutes to take this 25 point quiz. 1. [ 8 points ] Approximate the sum of the following series using the first 3 terms of the partial sum. Estimate the error involved in this approximation (i.e. tell me s = a error, or m s M , where s is the true sum of the infinite series). If using a calculator, only give the answer to 4 decimal places. X n =1 2 n 5 Solution: The partial sum using the first 3 terms is (2 pts) s 3 = 3 X n =1 2 n 5 = 2 + 2 32 + 2 243 = 16102 7776 2 . 070730 . Using the integral remainder test, we know that the error in approximating s with s 3 , i.e. R 3 = s- s 3 , satisfies the following estimate (3 pts setup): s- s 3 Z 3 2 x 5 dx s- s 3 - 1 2 x 4 3 s- s 3 - 0 + 1 2(3 4 ) s- s 3 1 162 Thus the error involved in the approximation using only the first 3 terms is at most (3 pts solution) s- s 3 1 162 . 006173 . 2.2....
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Winter 2006 - Reynold's Class - Quiz 4 (Version A) - Math...

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