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Chapter92006 - Chapter 9 Test 1 No Calculators Name...

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Chapter 9 Test March 17, 2006 No Calculators Name 1. Determine whether the following series is absolutely convergent, conditionally convergent, or divergent. Justify your answer. n = 1 H cos H n π LL n 2 cccccccccccccccc cccccccccccccccc ccccc 2 n + 1 H n + 1 L 2. Use the Direct Comparison Test H not the Limit Comparison Test L to determine if the following series converges or diverges. n = 2 H ln 2 L n + n 3 + 2 n cccccccccccccccccccccccccccccccc ccccccccccc 3 n + è!!! n 3. Let f be a function that has derivatives of all orders for all real numbers. Assume that f H 1 L = 5, f H 1 L = − 2, f H 1 L = − 6, f H 1 L = 18, and f 4 H 1 L = − 12. H a L Write the fourth order Taylor polynomial for f at x = − 1. H b L Write the third order Taylor polynomial for f at x = − 1. H c L Write the third order Taylor polynomial for g H x L = 2 x f H t L dt at x = − 2 H Hint : what should g H 2 L be equal to? L .
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4. Find the interval of convergence for : n = 1 3 n H x 3 L n + 1 cccccccccccccccc
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