Sol-166E3-S2009 - MA 166 Exam 3 Spring 2009 Page 1/4...

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Unformatted text preview: MA 166 Exam 3 Spring 2009 Page 1/4 NAME -®Rflg©i§t® KEY Page 1 / 24 10—DIGIT PUID Page 2 / 18 RECITATION INSTRUCTOR Page 3 /24 Page 4 /34 1 RECITATION TIME TOTAL / 100 i 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. . The test has four (4) pages, including this one. . Write your answers in the boxes provided. You must show suflicient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. . Credit for each problem is given in parentheses in the left hand margin. No books, notes, calculators, or any electronic devices may be used on this test. (12) 1. OO Determine whether the following statements are true or false for any series 2 an n=1 4‘25: each and Z I)”. (Circle T or F. You do not need to show work). n=1 NPC 00 00 (a) If 0 < an < 5,, for all n and 2 an converges, then 2 bn converges T ® 71:1 11:1 00 CO ()0 (b) If 2 an diverges and 2 bn diverges, then 2 (an + bn) diverges. T® n=1 77,21 77,21 ‘7“ J, J” 00 (—1)n—1 1 4—" n/ 9321‘; I") (C) n2 (1 22 + 312 412) S 215 , . . (T) F “:1 )‘i I ternc‘lffwb germs zi/iimoim WQOWW (12) 2. Determine whether each of the following series is convergent or divergent. (You do 4 fin each NFC, not need to show work). 00 R ”\ If; 7‘ (—1)"n! did? Q: (n+3)3 2 I m m) mam E __ (In-H m 21'], UL" E gmf‘ 2 v °° 1 (b) 2 :cos(—) me wgffrg) :2 i #- 0 n2 n—swo r“ __ N . n=1 led? fm’ Wavfigw‘“: Cixoeecaemf °° 4n + 1 '—”‘——“ (a9 if ;. LNU'I ;‘a wig“ (C) 7; 3n3 +2n+2 Miami i iii/:1 n?“ M MU»: Limi‘i inwwgmfigmmm CO h verge/nit“ ta (27) MA 166 Exam 3 Spring 2009 Name Page 2 / 4 3. Determine Whether each series is convergent or divergent. You must verify that the conditions of the test you are using are satisfied and write your conclusion in the small bOX‘ In Problems Bofioflc) Look [Am/1‘ lav conv, or OU‘V’. ‘Lf Wm], M: OH?) kw gambler“ 1 mm L»; mmwk If ‘< i W03.) chew—AA work: (smog 11331 3—7 015i): ffl‘r Lam m 00 a“? which {n gfiurugirwlfl w ,1»— : v Q mi (F3 we) " 7’ (#ng as“) V / J W (L «a ’ » W ‘\ Aw "m LA W‘s : > O a, 1m V“RW“Q fl ‘ an Ex?) “mi? mmloofiiéom “test, W (server; so (vi/(VENEVNM By the test, the series is CiJUQV’tg’fiJ 00 n b E _1 n _.__ ( ) “:1 ( ) n3 + 2 Show all necessary work here: A [ lQ/mqj‘.mc>} {gs/Wt? 5: «iris/l“ (i); bh CLQQNcn_$fw%? Lve Ix) , '7 his 723 7 an a m x W m, , ‘176 +2 ‘ ‘ grx'z, 1 3X? m X. m: (m mm w. I I 3 <0 ’53“ WE P“, am», WEE (4(2) Cw txmwaw 3mm 17% “$0 24 wwé’ai? filial“? l “CW 5’ WM Q g M By the mks § test, the series is cam; @"‘v”iéif€”li g MA 166 Exam 3 Spring 2009 Name Page 3/4 (c) Zsinfig) Show all necessary work here: Limit Claw WWW“ fitfii‘ii" . (11):“? gm stfm [til-"90 W T LN? W” @613 Q) By the li‘m; Qfl‘m‘fiffifll test, the series is Cfifl’l LEW"; oo 00 Y) 1 3 _ f (.L W :: 4 WC n: W 6? 4.. (—1)" m OO (6) 5. Determine Whether the series 2 is absolutely convergent, conditionally con— n=1 vergent, or divergent. You must justify your answer. y? w ) W cm “L w l _ M e A mm mm . 2 at“; Z w a " m :t tat/2. “my! Walt! ‘ hit} kiwi} {“ , CA3 s4 dy‘ugr%§ » $350? )6: .1: Co WW E UM b0 .3. a (1;) M tars ¥ by? v?” a g; r? ‘i‘ mgr, , my) (i a (Q Va”? is??? 33 ' mat-rifles?firxgjéio aw: aim? we sew/<2; 3333/1: » (5) 6. Find the Taylor series of the function f : em centered at a : 3_ Gwcééfi '3‘ 90 gal ‘ W {a}, \ngl‘lfi ‘51 l I; a a: Z (9 {wag} (V09 MA 166 Exam 3 Spring 2009 Name Page 4/ 4 00 . ~1 “3:” , (14) 7. For the power series E (—2—, find the following, showmg all work. “:0 n + 1 (a) The radius of convergence R. ‘3‘ MI W“ a?) )5?” l? f‘e inal- (mlmml‘w n+1 is ‘w I ‘3“ ' aria” I; Meghan» — >< fling; m ~> 1x1 the, (90?an m mam. x“ "#2 as was» Wflfim‘é'l: ‘ Swim mwer c i e- ~ ‘ I» a a»? lfilflmfl w «Wigwam. {Sm/ml, olive “be? 3+ My}; ‘Zij”‘w“wwj (b) The interval of convergence. (Don’t forget to check the end points). 09” V) y; @173 I When mm Z ('7‘) (ml) ,. Z in. a.» wégrifir‘“ “:30 WNW" v mgr} u+l " 3 Interval of convergence Gum Pam‘s? Vsi @\ w Vi) WLQ’ xv"??? :§ ' (my ‘1: AH; saw filler/"ll VGA“ ’ 1y? , ' ' H28 “M, l . £3 -. w gunman; (20) 8. For each function f find its Maclaurin series and radius of convergence. You may use known series to get your answer. — 1+2: W “AwNEEZm” )(x§<fl,)Rsl 1*? “5'50 ‘ a; W m n W Am a W) a: Zen flora W30 nfifl 1 d 1 1 l w Cl, IL (L my: m K m MW :Mb 2 W l lfiulll all: W filo 1 ~ g ism Q r “g?” hm! (1—$)2—“3L ’ ’_ X *‘ ’>< m «1. r { nil R '1: 4 (Q (C) :2 63;; 3 (Q in (I: Z a V) R :Q‘g / at)? :l. if?» if;wa gm 6 H320 iii 7 ...
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