2_Math141_Sample_C_Solutions

2_Math141_Sample_C_Solutions - WW5 I R;’IATH 141 2[EXAMII...

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Unformatted text preview: WW5 I R;’IATH 141 2 [EXAMII l SAMPLEC‘ 1 F. dl I. . I. l—cosx +oo ' m he "mt $11.11;; I2 ' 5. Find the sum of the series 2 {tan—101+ 1}—tan_1(n)]. Hz! a) w a) 1r b) 1 b) E J 1 4 c _ 2 c) E l 2 d) —- . ‘2 dfr d _._ ) 4 e) r1"he series diverges. 2. Find the limit _1i:nn(1 — mi “’0 a +3 6. If the series 2 an = 10, then find Iim ( u n-~+oo 2 a.) 0 “:1 b} 1 a) 0 c} -2 3 b _ "g ) 2 d) r: 13 e) 1n‘2 c) 2 d) ‘2 .1 l 3. Evaluate the integral / —5 dz. 3) 00 . ._1 :12 a) U '3: 7. Determine whether the series is convergent or divergent Z W. b) l H'.:I C) ‘1 a} convergent. by the root test. d) ‘2 b) convergent by the comparison test 3) The integral diVerges- c) divergent by the divergence test d) divergent by the root test +03 n—l 4. Find the sum of the series 2 2 . 6) divergent by the rat-i0 tth n:1 a) Z 8. For each ofthe series (I) and (II) given below choose the right. answer. 8 +90 2 +oc . — 1 1 + 3m :1. 8 (I) Z n (M) Z e—H— b — 4 ‘ 'n I } .1, “:1 Em. +1 112“ 6 c) 8 2 a) Only (I) converges. d} :f h) Only (II) converges. e) 4 (3} Both diverge. .d} Bot-h converge. e} None of the above. +m . . s . _1 n+1 _ ‘_ t 9. What is the minimum number of terms of the series Z --——( T33 D If It 1" Emerge“ "=1 we need to add to find the sum with 1 error I g 0.001? +30 (-1)“ 13. Z a) 3 “:1 n + 1 b) 5 +00 2 sin n (_l)n c.) 9 E R) d) 1] +00 n ' 15. —1 n e) 1.5 "2:; ) 2 + 1 +00 10. The terms of a series 2 an are defined recursively by equations 15. a] : 1 and ‘l + in n. _ . . a.“ H = M can. determine whether the series converges or dl- verges. n 17. a) The series converges by the root test. 1)) The series converges by the ratio test. c] The series diverges by the test for divergence. d) The series diverges by the comparison test. e) The series diverges by the ratio test. +30 22" II. The series 2 — is l “:1 n' a) convergent by the ratio test. h} cmlvergent by the root test. c) divergent by the integral test. d} a divergent geometric series. e) divergent by the ratio test. 1 nlnn +"XJ 12. The series 2 {1:2 is a) convergent by the ratio test. b} convergent by the integral test. e) divergent by the integral test. d) divergent by the divergence test. e) divergent by the ratio test. For Problems 13- 17, (each worth 3 points) determine whether each series is absolutely convergent. conditionally convergent. Cir diver— gent. Code on your acantron sheet: A - if the series is Absolutely convergent, C — if it is Conditionally Convergent, SAMPLE C.‘ MATH 141 EXAM II SAMPLE C 18. {15 points) Determine whether the given sequence converges or 19. [10 pts.) Determine whether the following integral is convergent or diverges‘ If it converges, calculate the limit. If the series diverges circle the answer. 5“ a) a“ = 3n+4 diverges l b) an = n sin — Tl. diverges c} an = (—1)""' diverges 4 A Lil an: diverges RCOSTI. n2 + 1 dive rgee' 6‘.) an 3 i n+1 converges to converges to converges to co 1] verges to (To nve r gas to divergent. If convergent, find its value: 1 lnz —,dx. f” a Justify each step carefully. a) EXAM Il- FORM A b)1.C‘2.D3.E4.B5.BS.B?.C8.D9.CIU.HII.A 12. 013. 014.1% 15. D16. (31?. A c) 18. a) Diverges; b) Converges to 1: c} converges 1-0 0'. d} converges to 1‘I e) converges to 0. cl) 19. Converge-5 to —4 {l ...
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