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Unformatted text preview: Chapter 9 Test
1. Use a Comparison test No Calculators
Direct or Limit 7
n 1 March 24, 2003 Name to determine whether n 20 n the series converges or diverges 10 n 2. Determine if the following series is absolutely convergent, 1
n 1 n conditionally, convergent, or divergent : ln n n2 2 3. Let f be a function that has derivatives of all orders for all real numbers. Assume that f 3 2, f 3 4, f 3 8, 3 18. and f a Write the third order Taylor polynomial for f at x 3. b Write the second order Taylor polynomial for f at x 3. c Does the linearization of f underestimate or overestimate the values of f near x 3 ? Justify your answer. 1 n 3n
n 2 n 4. Find the interval of convergence for : x 4 n 5. Find the interval of convergence for this power series : x 1 3n
2n 2 n 1 6. 7. Find the Maclaurin series for f x x2 arctan x 3 Determine if the following series is convergent or divergent : 1
n 3 n ln n e3 x , c ln cos x 22 2. 2. at c 3 6x 2
3 8. 9. Find the Taylor series for f x Find Pn x and Rn x for f x ,n 2x 2. 2
4 10. Let P4 x 8 3x 2 4x be the Taylor polynomial for f at x a b gx
4 Find f 2 and f 2 Find the second order Taylor polynomial for
x f t dt at x 2 f x3 3 4x 2
n 2 c Find the second order Taylor polynomial for x at x 2 11. Find a power series expansion for f x 12. Find the sum of the following series : n2 n ...
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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.
- Spring '09