166E3-S01

166E3-S01 - MA 166 ’ EXAM 3 Spring 2001 Page 1/4 /30 36 ....

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Unformatted text preview: MA 166 ’ EXAM 3 Spring 2001 Page 1/4 /30 36 . NAME STUDENT ID Page 4 / TOTAL / 100 1. Write your name, student ID number, 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. 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 or calculators may be used on this test. RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS ’ (14) 1. Circle the letter of the correct response. (You need not show work for this problem). 00 (a) Which of the following statements are true for any series 21 (1,, with positive 71.: terms? 00 (I) If lim an 2 0, then 23 an converges. n—me n=1 . an °° . (II) If 11m — = 1, then 2 an diverges. n—boo n=1 1 00 (111) If lim an“ 2 —, then 2 an converges. n—voo an 2 n=1 A. II only E. II and III only C. I and III only D. all E. (1) none (b) Which of the following series converge? 00 2.” (I) 11:1 00 3—1 . (11);:4_n (111)1——1— i—i+... 2\/§Jr 3\/§ 4J1 A. Ionly B. III only C. II and III only D. I and III only E. none MA 166 Exam 3 Spring 2001 Name _._____— Page 2/4 (20) 2. Determine whether each series is convergent or divergent. You must show all necessary ’ work and write your conclusion in the small box. (a) ; Vn:+4 Show all necessary work here: ’ By the test, the series is Show all necessary work here: . By the test, the series is MA 166 Exam 3 Spring 2001 Name _— Page 3/4 ' °° (—sr-l , (10) 3. Determine whether the series 2 T n=1 v is convergent or divergent. If it is conver- gent, find its sum. 00 1 - - __ n—1_ (10) 4. Consrder the series "2:5 1) n3. (a) Write out the first six terms of the series. ’ (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. cos(%) , . . lS absolutely convergent, condltlonally con— n=1 n2 + 4n vergent, or divergent. You must justify your answer. 00 (10) 5. Determine whether the series 2 The series is MA 166 Exam 3 Spring 2001 Name _~.__—_ Page 4/4 n :17” Zn 11:1 convergence at the end points of the interval. You must show all work. 00 ' (l6) 6. Find the interval of convergence of the power series 2 . Don’t forget to test for 1 (10) 7. Find a power series representation for f = and determine the radius of 1+95r:2 . convergence R. (10) 8. Find the Taylor series for f (z) = 1 + a: + 1:2 centered at a = 2. f (w) ...
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This test prep was uploaded on 04/07/2008 for the course MA 166 taught by Professor Na during the Spring '00 term at Purdue.

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166E3-S01 - MA 166 ’ EXAM 3 Spring 2001 Page 1/4 /30 36 ....

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