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

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

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Math 20D, Lecture C, Winter 2006 24 February 2006 Quiz 4, version B 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. n =1 3 n 6 Solution: The partial sum using the first 3 terms is (2 pts) s 3 = 3 n =1 3 n 6 = 3 + 3 64 + 3 729 = 142347 46656 3 . 050990 . 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 3 3 x 6 dx s - s 3 ≤ - 3 5 x 5 3 s - s 3 ≤ - 0 + 3 5(3 5 ) s - s 3 1 405 . Thus the error involved in the approximation using only the first 3 terms is at most (3 pts solution) s - s 3 1 405 0 . 002469 .
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