Statements - Analytic Geometry and Calculus - Solved Exam, Exams of Analytical Geometry and Calculus

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MA 166 EXAM 3 Spring 1999 Page 1/5 1] @ NAME GRADING KE y Page 1 /12 STUDENT ID Page 2 ht RECITATION INSTRUCTOR Page 3 /26 Page 4 /20 RECITATION TIME .| Page 5 {25 TOTAL /100 DIRECTIONS 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, 4 and 5. 2. The test has five (5) pages, including this one. . 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. wo @ (12) 1. Circle the letter of the correct response. (You need not show work for this problem). (a) Which of the following statements are true? Dif Ean converges absolutely, then Eon converges. N PC ne n= X UY) 10 1 and lim 2%} — 2, then © a, converges. N40 Gn net xan) If0 1 and 3 bn converges, then E on diverges. n= n= @® Tonly B. I and IJ only C. II and III only D. II only E. None le] (b) Which of the following series converge? % 1 — Lj Ninw' PT comp, test ©) eaayaP ot conv. Compare with 2 ty 1orviia test NPC M) Gs-—+a-t... conv, A. sew. tes OB AAS ey L,1,1 4 . eetenves be 4 nm n=0 Show all necessary work here: nel _2 net { n t rh-300 = yea @” (net)! < =e ies a) n3e NEA @ 4 ® By the vat to test, the series is Gonu erga ( <1 ) > VarF1 Show a necessary work here: ach & Comnpovet with Z an e- garcie E> Ne @ 4 < 4 => er TEND ees nat ne r . ‘ ov ie. @ @ @ —_ im ‘rail _ = Gm “a Live = =1 #0 | ye ®@ By the Lombar! san test, the series is = Cov UO spent e@ oc [ mit compari Son] 4 . MA 166 Exam 3 Spring 1999 3) @ (15) 8. Find the interval of convergence of the power series Lae wor 3 Name Page 5/5 cy x". Don’t forget to test for convergence at the end points of the interval. You must show all work. Gam alt zed catio 9 _test a TOS wei ml an 2 g (be | sr" |atin ML py i yi —3 99 Z " poe 37t (n+) sare X = 0; fay -~ «x @ =Uim ala) Ix} = BS © er F. SORES Comvenges (shosodulels) pow it og por IXIK 3 onder < 2 ” 2 <<. 1 3 ® 6 Al xs P BN ° =3 = ne canu. (p-series, pr? >) a n <— 7 ® ht ® test) — 2. nD 2° conv (alt sav. Te. At x28 yar Bttl ye F3) ~ 22 n ° fone obs.) @ 32x43 = 4 96 (10) 9. Given that er a1 aty se - a + a. t y ++) approximate the value of the integral ~* dx with error less than 10-5, using the smallest possible number of terms of the series. (You may leave your answer as a sum of fractions) 4 Zz & fa 16 xX 19 2 x x a CN dy a [Pete he ewan Co fe} > 4 = 3 s A ah - 88-2 NN ee A Oh plagging in amd ot ‘ egrat Toem bac en = os _ + 40 e_, oe “"s 40 3a00 Lee Qa pe for additional Levis 1 wae [ eo dx oO