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Unformatted text preview: Chapter 9 Test
1. March 18, 2005
„
∞ No Calculators Name Determine whether the following series is absolutely convergent, conditionally convergent, or divergent. Justify your answer. H− 1Ln H log5 nL2 n−1 n=2 2. Use a Comparison test HDirect or LimitL to determine if the following series converges or diverges.
n=2 ‚
∞ 5 + 3n 1 + 4n Let f be a function that has derivatives of all that f H3L = − 2, f H3L = − 4, f H3L = 18, f HaL Write the fourth order Taylor polynomial for f HbL Write the third order Taylor polynomial for f g H4L be equal to ?L. 3. HcL Write the third order Taylor polynomial for g HxL = ‡ f HtL dt
x 4 orders for all real numbers. Assume H3L = − 28, and f4 H3L = 48. at x = 3. at x = 3. at x=3 HHint : what should 4. Find the interval of convergence for : n=0 ‚
∞ n H2 x − 1Ln 4n 5. Find the interval of convergence for : n=1 „ ∞ xn è!!!!!!!!!!!!!! ! H− 3L n n2 + 1 6. Find the Maclaurin series for f HxL = x 3x HHint : Do you know a power series for ex ?L 7. Use the Integral Test to determine if the following series is convergent or divergent : ‚
∞ n=3 n Hln nL Hln Hln nLL 1 8. Find Pn HxL and Rn HxL for f HxL = log2 H4 xL at c = 2, n = 2. 9. Find Pn HxL and Rn HxL for f HxL = cos 2 x at c= 5π 6 , n = 3. 10. The series Hor, what is S − S6 ?L
n=1 ‚
∞ Hcos Hπ nLL n 2n converges. What is the maximum error of the sixth partial sum ? 11. Find a power series expansion for f HxL = x 1 iHint : Do you know a power series for j z ?y j z 2 1 −x { k H1 − 2 xL 12. Find the sum of the following series : n=2 ‚
∞ H3 n − 2L H3 n + 1L 1 ...
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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
 ANDERSON
 Math

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