271E2-F2004 - MA 271 EXAM 2 FALL 2004 Name —_— 1. Find...

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Unformatted text preview: MA 271 EXAM 2 FALL 2004 Name —_— 1. Find the limit of each convergent sequence. (a) a _1—10n+’n2 7“ 3722—8 ' (b) an 2 n — V722 — 2n. -2 1 sm (5) c =——————————. ()an 1—cos(%) 2. Find the sum of the series Z(—1)n+1 —3- 2". n=1 3. Determine which of the series converge absolutely, converge conditionally, or diverge. Give reason for your answers. 00 <a> Z —(‘1;Zfi‘ ” n=1 Z (_1)n2n3n nn 0° —1”n!2 oo _1 n (d) E 71((ln3L)2 (e) 2 003/271" 4. Find the Taylor polynomial of (1 + x2) coszv of order 7 at x = 0. 5. Find the interval of convergence of the power series i (217— 3)" “:1 n5“ ' $2 $4 $271. 6. The approximation cosa: ~ 1 ~ + +---+(‘1)n (2n)! smallest n needed to estimate cos(0.1) with an error of less than 10‘”. is used. Determine the 7. Find a series solution for y’ —— my 2 0, y(0) = 1. 8. lim 7” _ y . (m,y)—>(1,1) x2 — 212 9. Compute 37f;c +yfy + zfz. f(m,y,z) = my+yz+zx. 10. Find 631—7: at t 2 0 if 10 = sin(a:y + 7r), :1: 2 et, and y = ln(t + l). ...
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This note was uploaded on 09/19/2011 for the course MATH 271 taught by Professor Staff during the Spring '09 term at Purdue University-West Lafayette.

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271E2-F2004 - MA 271 EXAM 2 FALL 2004 Name —_— 1. Find...

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