Chapter92004 - ‚ n = 2 ∞ e n cccccccccccccccccc 1 + e 2...

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Chapter 9 Test March 22, 2004 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 n + 1 cccccccccccccccc ccccccccccccc n5 2n 1 2. Use a Comparison test H Direct or Limit L to determine if the following series converges or diverges. n = 1 tan 1 H n ccc 2 L cccccccccccccccc ccccccccc è!!!!!!!!!!!! 2 + n 3. Let f be a function that has derivatives of all orders for all real numbers. Assume that f H 2 L = 7, f ± H 2 L =− 6, f ±± H 2 L = 12, f ±±± H 2 L =− 24, and f 4 H 2 L =− 36. H a L Write the fourth order Taylor polynomial for f at x = 2. H b L Write the second order Taylor polynomial for f ±± at x = 2. H c L Does the linearization of f underestimate or overestimate the values of f near x = 2? Justify your answer. 4. Find the interval of convergence for : n = 1 H x 4 L n cccccccccccccccc cccccc n è!!! n3 n 5. Find the interval of convergence for : n = 2 n H x −π L n cccccccccccccccc ccccccccccccc 5 n H n 2 + 2 L 6. Find the Maclaurin series for f H x L = x 2 cccccc 2 cos H 2 x L 7. Use the Integral Test to determine if the following series is convergent or divergent :
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Unformatted text preview: ‚ n = 2 ∞ e n cccccccccccccccccc 1 + e 2 n 8. Find P n H x L and R n H x L for f H x L = x e x at c = 2, n = 2. 9. Find P n H x L and R n H x L for f H x L = sin x at c = π cccc 6 , n = 3. 10. Let P 4 H x L = 5 + 4 H x + 3 L − 8 H x + 3 L 2 + 6 H x + 3 L 3 − 3 H x + 3 L 4 be the Taylor Polynomial for f at x = − 3. H a L Find f ±± H − 3 L and f 4 H − 3 L H b L Find the second order Taylor polynomial for g H x L = ‡ − 3 x f H t L dt at x = − 3 H c L Find the second order Taylor polynomial for f ± H x L at x = − 3 11. Find a power series expansion for f H x L = x ln i k j j j j 1 − x 2 cccccc 2 y { z z z z 12. Find the sum of the following series : ‚ n = 3 ∞ 1 cccccccccccccccccccccccccccccccc cccccccccccccccc H 2 n − 3 L H 2 n − 1 L...
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This note was uploaded on 08/29/2010 for the course MATH 44323 taught by Professor Anderson during the Spring '09 term at University of California, Berkeley.

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