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5Cmt2s - Name 56 whens Perm No Section Time Math 5C Midterm...

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Unformatted text preview: Name: 56 whens. Perm No: Section Time : Math 5C - Midterm 2 March 1, 2007 Instructions: 9 This exam consists of 5 problems worth 10 points each, for a total of 50 possible points 9 You must Show all your work and fully justify your answers in order to recieve full credit, You may leave your answers in unsimpiified form, unless the emblem asks you to simplify o No books or calculators are allowed You may use a one—sided page of notes“ a Write your answers on the test itself, in the space slotted You may attach additional pages if necessary, 1. Consider the sequence {enhzg given by 815 32 1 3’ 9 ’ 27’ ' H (a) Find a. formula fo: the nth team an of this sequence in terms of '11, starting with n z 0' H- m Ox firmware. wipe/wan s mob We” 1 .__ qu ._._ 32m ,3 V ._,_ r; W ' ' ,._.._..,.. L1“ 3 M €13 Halo) 3. Ck?- LH‘ e‘czrm=0\-o= L1- WW“ -=—.. Lita/33‘" Hr W24) (13) Does the sequence {Graham} converge or diverge? If it converges, find its iimitn SW \H: 773'“ {’Huww A 3m 0-. km Gum: it,“ LHJQ/‘Qn “ZLQE \N—n co NJ: on w ((2) Find the sum of the series 2 an, or Show that it diverges. an 0c: 0'6 & ch- Z: We?“ = {:71 “=4: “55° we.“ ‘2." \"1/‘7: .. .21., \I?) 2, Do the series below converge or diverge? J ustify your answer's 00 Tl A film ,ijv» QM —,—, 5);.“ m -\ 71 O “”4350 RANK! 9mm gum-W ‘on. WW“ ‘\-br-M Ark/571'- “° \ ~ ~— ~ "Mm _.._...... 3 0x ‘3 Wow}. wx 5") W :V‘511 \ V\=~.\ 3. Find the radius and interval of convergence of the power series if: 2”($ ~1)" 27L“ 1 71:0 emgwma in“ \“*‘\=*— MM\1"*‘(x—n"‘"“/Qcm-\3\ 1*“ w M“ We QMWDVQNW QLJL. ”fl -.-_ m. 1(x~\\'U—V‘"‘3 V'\.--‘\D<J ln+\ .5; __\ ~ LUV-'2. \x \v-Dérmk 1n+\\ ”-1 Clix-M <\ ....\ _ 9.3.. w..\w""~“ “:3 .4“. ~ ‘ W ' “2;; iiCnfz? __fi_ 2:; "if: w. 0W\ gig: GM “7”) Rr “7"": \fi Emma“??? 7 0' 'SMLL 0&1“); ‘9 v%ja“tc €me m2» \m a“; “>3:th er m w». W WW4“: mmyge: LAQ er AWWMS WM W U? Ktz/z- i: iiii/QA— ”Eh Dwgggg; at) mmgwtw'fid W“ mach Wm: QM”. Ki" 7 733.1 A: 2%? .._ ”\iZTVL“ éivwifia. Qw- “7‘4 4 Q“, $_C.fi-::. [1/1‘3/1”) 1 4‘ Find the Taylor series for f (51:) = W, centered at m = 1, and determine its radius of fi (For full credit, your answez Shouid be written in E—notation To receive partial credit, you may write out the first five terms of the Taylor series.) :: {"1" m QM ==\ convergence \ “fl: 3:: 1 t -3, ._ U ; .._.._ {:‘(x=—-—;X I?" N S; 7“" 1&“&x\zk~-‘;)L~%3X““” :27 mm (“a 41-2». ‘E“‘b<\=.(-%:\E~ %\~%3x“’“"~ :2» WW: weaxa I?“ km 9&- am:- akviL-Nx‘fl‘" m» W0 : G» at $9 éfib—fia . . ~--L “— ?WM stag): L-«m‘wlfim‘l Gw mm '3": q 3: x-—\\L—% (x—W’Jr 1f (Kw-D +... ”\$”§LX"Q* 3L T6" [3 h W“\ ELE— Q-\\V\[.3.g..,{1“ Q/z‘ ‘ \ \ R.C’ . :7- “_;}Do \ (Ln-t ‘\'=- &me \L’nn1\ \‘3‘S“'LM“\\L1V*\\/ givi‘ LW+\)\- l '5 ‘3 ‘(Q-WAU‘QDHKAM)‘. \— flA‘M \lUWQ \ __'____'__'___._.—--—-—--——"‘ .- ‘Ju: ‘M \ \‘3'9 .‘ >[1U\*‘\\ {lm*‘\ul"\.fl\‘ (\me XW+X “"306 \ “An/v» 7-- “H ’L 1:; \ = L‘Q’V\ 2mm “"— JXL’XBO 9.. L t n»- no 3:11 n+1 00 5‘ (3,) Find the function fix) Whose Maclam’in seIies is 2 71:0 . (Hint: Multiply the series by a: and then differentiate) N 9i w“ :5 fiQx£(..m--= fifl; as?) vx-H 90 fl 1 z X *‘—‘ ; {MK I W15 (‘-\<>< <1) m K“ firm:- KEN '3 Hm: 81%;"fo = hum—M H. [gr who k, MW." PM: (L: 0%[M=O=-ln\+t=0+u:g :37 C29 ‘14“. VHJQ': "\Aq l\-—-X\ . CTWW‘xcojléj' Ms Wm 1%. M?“ “‘ -. ' Albhxel m-EXm©.3°+\‘>*- Wrufi, Wk. RMCX L..\ < x s \ 3 WM X¢® Name 00 M (13) Use (a) to evaluase the sum ; (n :1)?” m \ m .4... .L vx ._ \ Z (““31“ T" Z W“ '3” .. SEE A.) “no fl~0 2: "M ' 1/1.. - “Zln VL. .. '2. \n L ...
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