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166E3-S07

166E3-S07 - MA 166 Exam 3 Spring 2007 Page 1/4 NAME...

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Unformatted text preview: MA 166 Exam 3 Spring 2007 Page 1/4 NAME 10—DIGIT PUID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. Write your name, 10—digit PUID, recitation instructor’s name and racitation time in the space provided above. Also write your name at the top of pages p, 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 (12) 1. Determine whether the following statements are true or false for any series 2 an and 71:1 ' 00 bn. (Circle T or F. You do not need to Show work). :1 n 00 00 (a) If 0 < an < bn for all n and 2 bn diverges, then 2 an diverges. T F 71.21 ' n=1 (b) If 0 < (1,, for all n and lim 9%: = 2, then 2 an converges. T F n—>oo m “:1 00 00 (c) If 2 an diverges, then 2 lanl diverges. T F n=1 71:1 (12) 2. Determine whether each of the following series is convergent or divergent. (You do not need to show work). .1 . (a); (ﬂ), : (b) 32+. ——l :3 MA 166 Exam 3 Spring 2007 Name Page 2/4 (30) 3. Determine whether each series is convergent or divergent. You must verify that the conditions of the test are satisﬁed and write your conclusion in the small box. (a) Z <—1>"-1 1‘17” Show all necessary work here: test, the series is “92W n=1 Show all necessary work here: test, the series is MA 166 Exam 3 Spring 2007 Name — Page 3/4 (c) i sin ~1- n=1 n Show all necessary work here: test, the series is (12) 4. Determine whether the following series are absolutely convergent, conditionally con- vergent, or divergent. (You do not need to show work). (a) Z 317:1!” n=1 MA 166 Exam 3 Spring 2007 Name —— Page 4/4 11. 00 (16) 5. For the power series Z x—, ﬁnd the following, showing all work. “:2 Inn (a) The radius of convergence R. (b) The interval of convergence. (Don’t forget to check the end points). Interval of convergence t (9) 6. Evaluate the indeﬁnite integral / dt as a power series and give the radius of convergence . t8 (9) 7 . Find the ﬁrst three nonzero terms of the Taylor series for f = lncc centered at a I 2. ...
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166E3-S07 - MA 166 Exam 3 Spring 2007 Page 1/4 NAME...

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