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166E3-S2009 - MA 166 Exam 3 Spring 2009 Page 1/4 NAME...

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Unformatted text preview: MA 166 Exam 3 Spring 2009 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 testhas 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 E can 11:1 00 and 2 67,. (Circle T or F. You do not need to show work). n=l ' ()0 ()0 (a) If 0 < an < 1),, for all n and 2 an converges, then 2 bn converges n21 n=l n=1 12.21 00 00 00 (b) If 2 an diverges and 2 bn diverges, then 2 (an + bn) diverges. 71:1 00 _ n—l (c) n; fi—1.2L—~<1—a+a—a> 32—15 (12) 2. Determine whether each of the following series is convergent or divergent. (You do not need, to show work). (a) Z (jinn! . n21 °° 1 4n 1 (C) 2:31 m TF TF TF MA 166 Exam 3 Spring 2009 Name Page 2/4 (27) 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. Show all necessary work here: _—I By the test, the series is 00 n b —1 7" ——— <>n§=jl( > ”3+2 Show all necessary work here: By the test, the series is MA 166 Exam 3 Spring 2009 Name m— Page 3 /4 (c) Emmi—2) 71:1 Show all necessary work here: By the test, the series is (4) 4. Z 43”: 72:0 . . °° (-1)“ 6 5. Determine whether the series ( ) 7; \/7L + 1 vergent, 0r divergent. You must justify your answer. is absolutely convergent, conditionally con- (5) 6. Find the Taylor series of the function f(x) = e” centered at a, = 3. MA 166 Exam3 Spring 2009 Name . 00 (#1)n$n 14 7. F th 0 ries ——~———~ ( ) or e p wer se ”E20 n + 1 (a) The radius of convergence R. Page 4/4 , find the following, showing all work. (b) The interval of convergence. (Don’t forget to check the end points). Interval of convergence (20) 8. For each function f find its Maclaurin series and radius of convergence. You may use known series to get your answer. (a) f(x)=1:$ 1:333}: 7R: (b) Ax) = (13302. (Hint: 3‘53; 1; = 3:13—55) (13:02 :2 (c) me) = e3” : Z , R: (d) f(a:) =sinsc. Sim: Z ,R: ...
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