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Exam 1 Solutions

# Exam 1 Solutions - Math 408D Exam 1 02I06I2008 Print Name...

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Unformatted text preview: Math 408D Exam 1 - 02I06I2008 Print Name: SO [ (”Uh mg Sections 58100, 58105, 58100 Your section number: Do all work on this exam paper. You may use the backs of the sheets if you need more space. Answers without sufﬁcient supporting work will receive no credit. 9O ‘ d x 1. Explain all the reasons why the following integral is improper (10 points): L x- (x c; ) m ”Fm/LOWUM {US} 3 m is discomﬁummg (and ‘m rf‘ocf‘ {AM Val/Hug Mgwpﬁlu) M X50 W 5c: l. \Qoo Ci WmWLowr ﬁMPOH/[T M‘ﬂ \C‘:‘-—l 5’] [lg/13:44 tacit/118W. AUG) 1"“ iﬂrCVthﬁ—Q I: {pk/life. ”D; game W5 ryVUWi/Vl) you‘d Min W Li- imrqmag wl Z .9“ ’ R94 Maw/kw?) ‘(WQQECXQAK == fz'lﬂc’odx1‘ f%¥(><)d¥ +jl jﬂtr)dx+fer(x)dx, 0 All «fwr immoral; 0W? Wm??? M 2. Find the iimit(10 points): £33190 (7:: 3 m if) 6K l {WWI/1. )Q-l T 3) am (@150 ((“VW‘ .- . 1M ":5 QL‘H'VV‘ 0) {‘guﬁﬂ’lNNX—a his -— ,J_ 3 Determine whether the series converges. if it converges then find the sum of the series. a. (10points) .ZL ijﬁ 2H+l Li 21/] V‘ VI EN @“202 2 ZCZL)’: So 2"] 14 14 V\ In D. _ LP i ....] — (*1) '2.“ (mi) ( 3 w. W L. %W%m ‘ﬁv—st—vt qfr., ﬁance JUM q“ ¢ 0 [ {Kr/I041, (m. a.“ wow Ni“[email protected] i/\ No Mﬁ/O W was Aiwxgg)\wa HM 'DIFquTa/Ih ““ 'I‘x h k f b (10points) .2 (2)“ m3 (3 a WWMC— £4»er 4 3’” r ——2 J_ or: —~-——— w- W‘“" 4+3 4: —~}; if: 3 ir|:%<l So WWIFMWWK) .J ,L a "_____Q_’_____ h '6 __,___3'_:__j_ _ ‘2— '” r " so (0 \"r l” ("3:5 3*“ 4. (10 points) Determine whether the series converges. Give valid reasons for your answer. Zk—i)“ Yl=i Vi if)“ )R For partial credit, find Him . x930 1 0 m :2) m aim-m3 W ZC-H“ a, W K b: 27‘ 1W )0“: ”m \$3:le ”7;" ,m h [o [rape W990 if) new a .06 R“ r Qél . E n ‘ W in cm 00 \$50M :3"? L’W‘ will/(Arc W990 9M1” ‘6 (BU m A"[’l’€VVM1ﬂ/& chfa Tmf/ +€U {PM/\$54 WW 5. Assume that the series of problem 4 does converge. Find the smallest value of n such that if the nth partial sum is used to approximate the sum of the series, then the error is less than 0.01 . (10 points). 3;? Sin rm wd +9 a/ppmi‘majl S:— ZC’D [£74 ) W [Ail i .—~ rl/l I HJ/Ulymi/Iw Um Mm Lhﬂ lomﬂn [gt/1+1 m W6 Mdgﬁﬁm V‘ W M bin—f 0’0' ﬂ _ w z ; rxmtl ”1 b; - [00— [cm 0’01) W amougti 3 3 l, W; ‘ L'3: [‘5 : Loco :— (”003/ ﬂoaaemﬁf” O 6. Determine whether the series converges or diverges and state the reasons for your answers. (10 points each) 00 h a. Z: (:11) n-ro .‘F V\ 1.1m \qml 2: {A‘ibo s. 121M 2+3“ __ wﬁm B‘FLIA a ,3. ,H ___ 2’“ L)! So :04?) D {agoTk Leif w 2n1—I b' g haw—+43 9‘0 As WWA 2 {AL “'“l r 2m’k“ [r “M hoist/{176K (=3 “:40 Wﬁk 1A”-7 rt» .L ___ Hm 2* M ‘Imru% \4— LVfii % 2+2m a“ , £g+2m ) W L r .__+ (W m 3 hﬂk 3s n+2 Vv—"I M 0\ 2 1000 C3 ' MM V‘ m)” ) O‘M’f“ : 1 00 a _ (WED! [W at“) .. “M [000M] Ml, w—m '- V‘ m €990 (INFO) [001) .2: W1 “900 -— Wak vvtl ﬁe 3L L<| 5‘0 W W J W ) d :2 m (313mm); Meta: 1:1 start: a»? 2 We We mug/vi Km chmL‘WW'H ”[2 9°) .00 _,J_/— (i "”‘ m M ’"T’ "L g x ﬂux)” Wm X M X M a [Mg/:1) (A: M1 5 3 wwmmﬁ) “gbb ...
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Exam 1 Solutions - Math 408D Exam 1 02I06I2008 Print Name...

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