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162E3-F2008 - MA 162 ‘ Exam 3 November 2008 Name...

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Unformatted text preview: MA 162 ‘ Exam 3 November 2008 Name: 10—digit PUID: Lecturer: Iiecitation Instructor: Recitation Time: Instructions: 1. This package contains 14 problems worth 7 points each. 2. Please supply a_]1 information requested. You get 2 points for supplying all information correctly. 3. Work only in the space provided, or on the backside of the pages. Circle your choice f0r each problem in this booklet. 4. N 0 books, notes, calculator or any electronic devices, please. AD LLB 3.4 4-0 {—6 6D 7.4 35' 0L4 /0,E‘ ,. ..._~._-...V_—n-—‘. _--, ', W. ‘ “—3 MA 1. lim 162 3n+1 n—roo n2 + 4(—1)" A. B. C. D. 1/4 3/4 3 0 Exam 3 E. The limit does not exist 2. Which among the following series converges? III. 3.5.095? All three Neither Only I and III Only II Only I November 2008 ' v ~- -fimfim:v« MA 162 Exam 3 November 2008 3. Evaluate 10 20 40 80 160 5___ ___. ___ 3 9 27 81 243+"' A. 3 B. 5/3 C. 15 D. 10 E. 10/3 4. For What values of 1} does the series converge? A. p21 B. p>1 C. p22 D. p>2 E. p>0 MA 162 Exam 3 November 2008 2—m \/'r_n+3 ' 00 5. Which is true? The series 2 m=1 00 A. converges by comparison with Z 1 /\/m. m=1 00 B. diverges by comparison with Z l/fqfl. "1:1 00 C. converges by comparison with Z 2"". m=1 00 D. diverges by/comparison with Z 2"”. "1:1 E. The comparison test is not applicable. 6. Which statement is false? A. If {an} is a bounded, increasing sequence, then it is convergent. 0° . B. If 2 bn is convergent, then Jim bn = 0. "=1 fl—POO 00 C. 27'" diverges when |r| Z _1. n 1 OO 00 D. If 2 bn is divergent and if 0 s an s b”, then 2 an must be divergent. 11:1 11:1 00 E. If an > 0, 6,, > 0, lim an/bn = L is finite and positive, and if 2 bn is divergent, fl—POO "=1 00 then 2 an must be divergent. n=1 MA 162 Exam 3 November 2008 w 7. For the series 2 (—1)"’k, the partial sum 35 equals k=1 A. —3 B C D.5 E 8. For the series below, which statement is true? 'I- SON-1V; °° (—1>k ' I II. ; l k; «I? ; III. :0: (—1)me-m. g m=0 " l A. All are conditionally convergent, none of them is absolutely convergent. B. All are conditionally convergent, III is also absolutely convergent. I C. None of them is conditionally convergent, III is absolutely convergent. D. None of them is absolutely convergent, II and III are conditionally convergent. E. II is conditionally convergent, III is absolutely convergent. MA 162 Exam 3 November 2008 00 9. The set of a: for which the series 2 e‘kz/k! converges is k=1 alla: x51 m<1v $20 913.093?" $>6 (2n + 1)" 00 10. The series 2 W n=0 A. diverges by the alternating series test. B. diverges by the integral test. C. converges by comparison with 2 2/71,”. D. diverges by the ratio test. E. converges by the root test. MA 162 Exam 3 November 2008 7 oo 11. The radius of convergence of the series 2 Tran/(n + 1) is 11:] A. 0 B. 00 C. 1 D. 2 E. 1/2 00 12. Given that the power series :3 (x— 1)”/ {WE has radius of convergence 1, its interval ' m=1 of convergence is A. [0,2] B. (0,2] . 0. [0,2) D. (0,2) E. none of the above MA 162 Exam 3 November 2008 14. Starting with the power seriw of 1/ (1 + 21;), compute the power series that represents 1/ (1 + 21:)2. A. i (2x)2m m=0 00 B. Z 2m(2:1;)m m=0 C. 2 m(——2)’""1:1:m"1 m=1 00 D. Z m2.‘Z—"r‘:1:2m_1 m l 00 E. Z (_1)m22m+1$2m+1 m=1 -- 'nli‘ujff‘m'f Hr, \v-‘rw A ...... ‘r' _ n.- .' ...
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