166E3-S2010

166E3-S2010 - MA 166 Exam 3 Spring 2010 Page 1/4 NAME...

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Unformatted text preview: MA 166 . Exam 3 Spring 2010 Page 1/4 NAME 10—DIGIT PUID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. Write your name, 10~digit 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. N 0 books, notes, calculators, or any electronic devices may be used on this test. (12) 1. Circle T if True or F if False. You do not need to show work. 00 (a) If "limo nan :: 5, then 112—31 an converges. 00 (b) There is a convergent alternating series 2 (—1)”bn, with bn > O, and such that lim 6,, 7e 0. “1 n——>oo DO 00 (c) If 2 an diverges, then 2 Janl diverges. n=1 n=1 (12) 2. Determine whether each of the following series is convergent or divergent. You do not need to show work. 61/71 (a); n n=l DO . 2 + smn (b) E —~———2 n=1 n 00 (e) Z (21“ — 1)” n=1 TF TF TF MA 166 Exam 3 Spring 2010 Name W Page 2/ 4 (27) 4. Determine whether each series is convergent or divergent. You must state the condi— tions of the test you are using and verify them if they are not obvious. Write your conclusion in the small box. (a) Z 1.3-5...(.2n—-1) Show all necessary work here: test, the series is Show all necessary work here: test, the series is MA 166 Exam 3 Spring 2010 Name W“— Page 3/4 2 (“2% Show all necessary work here: test, the series is 0° _ n (10) 5. The series 2 754116))“ satisﬁes the conditions of the alternating series test. n=1 (a) Write out the ﬁrst ﬁve terms of the series. (b) Use the alternating series estimation theorem to ﬁnd the number of terms that we need to add in order to estimate the sum of the series with error < 0.0001. terms (5) 6. Find the Taylor series of the function f = e‘8 centered at a, z —1. MA 166 Exam 3 Spring 2010 Name _——__ Page 4/4 00 (14) 7. For the power series 2 E”; (x + 1)", ﬁnd the following, showing all work. n=1 (a) The radius of convergence R. (b) The interval of convergence. (Don’t forget to check the end points). Interval of convergence (15) 8. For each function f ﬁnd its Maclaurin series and radius of convergence. You may use known series to get your answer. 1 1—313 (a) f (93) = (c) res) = ...
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166E3-S2010 - MA 166 Exam 3 Spring 2010 Page 1/4 NAME...

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