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166E3-S06 - MA 166 Exam 3 Spring 2006 Page 1 4 NAME...

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Unformatted text preview: MA 166 Exam 3 Spring 2006 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. N0 books, notes or calculators may be used on this test. 00 (9) 1. Determine whether the following statements are true or false for any series 2 an. n=1 (Circle T or F. You do not need to show work). 00 (a) If li’m an does not exist, then 2 an is divergent. n ()0 n=1 (b) If 0 3 an 3 fi for all n, then 2 an is convergent. n=1 00 . an+1 . (c) If nllIIl an [ —— 1, then 321 an is convergent. (12) ' 2. Determine whether each of the following series is convergent or divergent. (You do not need to show work). (a) 2 3:21 MA 166 Exam 3 Spring 2006 Name _——— Page 2/4 (27) 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)"-1ne~% Show all necessary work here: test, the series is Show all necessary work here: test, the series is MA 166 Exam 3 Spring 2006 Name —___ Page 3/4 (C) E nlhn n=2 Show all necessary work here: ' test, the series is case) —— is absolutel conver ent, conditionall n2 + 4n y g y 00 (10) 4. Determine whether the series 2 n=1 convergent or divergent. ' _ 0° __1 n—l (9) 5. Consider the series 2 n=1 (a) Write out the first five terms of the series. I (b) Find the smallest number of terms that we need to add in order to estimate the ‘ sum of the series with error < 0.01. MA 166 Exam 3 Spring 2006 Name —_—______ Page 4/4 2 n n ‘ 4) x , find the following, showing all work. , , 0° (— 16 6. F th — ( ) or e power series 3:1 fl (a) The radius of convergence R. (b) The interval of convergence. (Don’t forget to check the end points). Interval of convergence (10) 7. Find the power series representation of (about a = 0) and give its interval of convergence 1—21: Interval of convergence (7) 8. Find the Taylor series for f : e“: centered at a = 3. ...
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