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Unformatted text preview: MA 166 Page 1/4 Exam 3 Spring 2008 NAME
10—DIGIT PUID
RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. Write your name, 10digit PUID, recitation instructor’s name and recitation time in
the space provided above. Also write your name at the top of pages 2, 3, and 4. 2. The test has four (4) pages, including this one.
3. Write your answers in the boxes provided. 4. You must show sufﬁcient work to justify all answers unless otherwise stated in the
problem. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin.
6. No books, notes, calculators, or any electronic devices may be used on this test. ‘ . 00
Determine whether the following statements are true or false for any series 2 an and
71:1 (12) 1. 00
2 bn. (Circle T or F. You do not need to show work).
11:1 00 00
(a) If 0 < an < bn for all n and 2 bn converges, then 2 an converges.
11:1 n=1
00 (b) If lim an 2 0, then an converges.
7). +00 1 n: 00 00
(c) If E Ianl is convergent, then 2 (—1)"an is convergent.
11:1 71:1 (12) 2. Determine whether each of the following series is convergent or divergent. (You do not need to show work). 0° 712—7
(0) Z n3+2n2—1
n21 TF MA 166 Exam 3 Spring 2008 Name — Page 2/4 (30) 3. Determine whether each series is convergent or divergent. You must verify that the
conditions of the test you are using are satisﬁed and write your conclusion in the small box.
°° 1
a
( ) 7; m/lnn Show all necessary work here: test, the series is Show all necessary work here: test, the series is MA 166 Exam 3 Spring 2008 Name _—_______ Page 3/4 2 (e) Z (—1)” ” n3+4 Show all necessary work here: test, the series is 00 2271+]
(4) 4. Find the sum of the series 2
5n
n=1 (12) 5. For each function f, ﬁnd the Maclaurin series and its radius of convergence. You may
use known series to get your answer. (a) f (16) = 0362"” (b) f (a?) = sin($2) MA 166 Exam 3 Spring 2008 Name —— Page 4/4 00
(16) 6. For the power series 2 n3 (m — 5)", ﬁnd the following, showing all work.
71.20
(a) The radius of convergence R. (b) The interval of convergence. (Don’t forget to check the end points). Interval of convergence 9) 7. Write out all the terms of the Taylor series for f = 1 + (I: + 3:2 centered at a, = 2. (5) 8. The Taylor series for f : lnzc centered at a : 2 is (—nnl = Ina: :ln2+ Z zit—(n) (x— 2)". Find f (166)(2). Leave your answer in terms of powers and factorials. f(166’(2) = ...
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This note was uploaded on 09/14/2011 for the course MATH 166 taught by Professor Staff during the Spring '10 term at Purdue.
 Spring '10
 Staff

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