Chapter92007 - Chapter 9 Test March 18, 2007 No Calculators...

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Chapter 9 Test March 18, 2007 No Calculators Name 1. Determine whether the following series is absolutely convergent, conditionally convergent, or divergent. Justify your answer. n = 1 H - 1 L n 3 2n + 1 ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄ n H 5 n 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 4 n + è!!!! n + 2 n ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ 3 n + è!!!! n 3. Let f be a function that has derivatives of all orders for all real numbers. Assume that f H 3 L =- 2, f ¢ H 3 L = 5, f ¢¢ H 3 L = 8, f ¢¢¢ H 3 L =- 12, and f 4 H 3 L = 16. H a L Write the fourth order Taylor polynomial for f at x = 3. H b L Write the third order Taylor polynomial for f ¢ at x = 3. H c L Write the third order Taylor polynomial for g H x L = 3 x f H t L dt at x = 3 H Hint : what should g H 3 L be equal to? L .
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4. Find the interval of convergence for :
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Chapter92007 - Chapter 9 Test March 18, 2007 No Calculators...

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