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13thsol - I. “ Pertiel fractions improper integrals...

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Unformatted text preview: I.» , “- Pertiel fractions, improper integrals David Pierce December 24, 26307 Problem 1. Compute the foliowing indefinite integrals. I ‘ I . I. . . ‘ i ‘ ' - V‘ ' 3 _ ' I - 4 _ 3 4 2 W 1 (3)] 1r: 3 dm II , 33; + :2: 332+ dIIII mE—«m—S m4+333+4m2+3m+14 5“: 433+9x2+8$+3 (b) fmdm Wmd $21”?1 . (a) m4+3m3+4az2+3m+1 3 3‘3 (6} fame?“ Problem 2. Assuming deg f < 8, analyse ,\I no f" ' {292 + 4a: m 5)2 - {$2 Jr 4:12 + 5)2I, . “it: as a sum of partial fractions. (No need to compute the numerators.) Probiem 3. Evaiuete the foélowing definite integrals. 32 2 dm ‘ W d2: (a) [O 1+m1/5 (b) j; 2+s‘1nz Problem 4. Evaluate, if possible, the following improper integrals. Problem 5. Determine whether the following improper integrals converge. e f: °° clan . m M o) 5 w I I a) IAIIIII b ‘e if“? L, x X3 '" x - 3% :? X2 ~ xmé ' KBMA yam}: ué g .K3*A1‘éf\x+i :gmfi‘“ g: X4! + 626% g .. £3135 : x «u .1, c; m 536% Q Mm‘mwg New “Qifimm A; mg, "w' "W “*5? {ergfifi} {w} 56%;) :3 «3 50 “M- Jig .-: SQC-MW M +65 9/9 gig “in 6 4/5. .é‘x fi2“X—(§ Km”; fie“? '2“ J ““ X2"? K i~ g } ‘ .. 4% Mag! an 4 inn”, + ‘ ‘ . ' x v. 33% fi WP _ -' {any m; K'““¢“V“H 35 MW; v” g?“ mgzcfiimflwémim W 5 mw‘i'mm J .2, 3“ &E’“?’«F+E - Mkva . ' l (j w W _ x K “L- ‘h ‘ Kl‘t‘ X—H} ‘* 5 L. L 2_ L {if—4%) “mg?ng .3" j, [Vim‘x VX3913! u..- wg-am C'Vfi‘i‘m f—C’ Ila/9&1 Hum!» dxgviw waw'fim mfg, gawk 535* 0 . MWWW I” 7%? 4mm gisvm w 11;. -'ir3/’-“"‘j°’-c’oé y“. - 2.“ -' "'4';- , - ., w 5w» fie: W‘Wil w 2 {away 1%? .' i +017“ U, Sm?“ .., 5 Staci u aid 4 (law? £32, Wu m w - 3 I figu'lu I 5’3th 3 “film” , fiee‘i/wifi Qua; @WLW on, 3% “W if %? «vw‘m Sign!” " 3 ('3 Swain; M (Q! , 594 W “fin...” WW 3 g” +- - 3 {E cram 3 - . ' W32“ . _ %' 3x5 '79 2: Tank‘mm...,u.1,5,3Wzmwxwwunmmmwnmmwm'“flma‘ + C Eu; mmfig (mgr- ‘- - "‘ .‘L , -2“... - “m '- ’3 2, er 3m; is L 3 Y1 L mwwmmWMWN~mw r m w e, .__'_,...u , 3 g; \m, we "LE T Cw ~ . g! xix; Xqfiixg ?~me¥»30{~£; Rm. all. ‘ 5 . )Q‘milqg; ‘ . gxfifigleg’gnffi f _ . LL». ,mfimmmiwm flimsj “l” r)v\|ui~f~Q “fig-K‘afiémfiwfiwéfi u clu "sap? + 341%55K‘53‘)0£’$ A9344.” ‘2? gfly I , jam 1» , " {x1“+LK~K—’}é~~{x1+ 61H?) (1+SXL-<.x«l}2- (Kimmy/3‘“ q, '9 Vb (mm-(.14) _ “WM-6 N‘Wum‘héa 53 Rafi-m m A ““WW Wm Frude wg i, . L ‘1 .V “Maj M” E’VWM‘" Wigs!“ («29:»ng z + + waH WWW- CMMH gm 5);- -u‘fiul V‘“ ‘ W E! "m: - ~ .nd L . 7, ~ u-mq miwmw.,.WflegmmkmmwrmmwmflrMnM- - m ‘mnsmm-mpwWw—WJWWW.”uwumww. n—«n *w l—tSMA D 3 3m _ U “IL-f" 18%;; {mg-‘5; 0- 3" 2' 2m? {\Q/fl'fi; g m a 2* £3. 1., fl 1 i J: S Hwém wwxfmm‘w (jufi 2;“- ;r. —J- O l. +~ 3. 4&ng ~ if wfia": 2" ml 1 (051% .tr' ’2 Z (32» fi "if g :2: 1"“1'1 aw m-«Mgwx u: f 1&1“ M.» “ [HI-1) M. , “2;, cm a .3" m r: I ELHMM imfikah ' O i " my ~ 8 ('12: W W ' «Mm —— 4: (a ‘ ’L “ 8 WW}; 0 H "U *4? Q ) a:- 3... UF€‘\€/fl3—£%W’g»_fl 2 $(EM-m 75;) { V1 - r3 0, W3 3 6-; {Mean km» S I ' éfi'y WNW 7%” W“) syn we; i EU *1“ M X3 x3» 0 a 1... HM gwagemmw 3 “I _ fiww‘ “E 3i MMQ‘ [‘3 x ‘ a ‘ J3 -3 -\}w~ S x the "e E'W g M JR WW0“ 5‘ E‘WOA’ 8 a 3% r k 'M ELEM xfimglwmm I g" “.2: m fl @9534" “‘3” g fiw-wn‘“ \ ‘ .. fl ‘ “+3 J, 0 wk LVN-a Irv-L. + ulna m w {W l 'W‘“ 3 193%an g” 2 mg i fian" ‘ PER 39hrsz ‘F'W h V 1, "(1 “Li, : u M g 0 n ma a” «21% l O S at A wag, QEMflzg Qn'l': 5 ohm (Law/(22%", fl X3 w) «"1 Em «m NM 8 Q ’50 B o ’ w M m S M +3 ¢Mdfihflsifim Jam % :3 MH- M" a “g 3" ‘6’ I 3 91x1 "‘ 3‘3 fl ~— x e“ M £6 WC I o r M; $3 15. m ' ¢ x I “M WWI“ ' M S x 2. “a 2. mg? + ’1‘ “13%” “NM-7571 ‘X’jd’x ( I X a x, a [A23 a: “x; if” PM” “ x U .NW bmwm ‘3‘“ (‘3) I “Let‘vi—ui xi" ‘9’“ 0 .2 2. ‘2' i an it “’ "MN ' .2, x W1 A. .1, M" AM 53‘ L ML "g r ~+ T «e« m». m" 2. d. Qw- 2;, .L wk “1,. i 1 2,, W :20 I w W 3 . Swhgfi ) éfi $ thg éxg 5% mafia Kg X my; ff» 4’ affix CAD \ S $36 “:3: i... o “w a K Lu: LN» Sax” i&“lw‘n “24/ Q?“ & (33A 7' r I, 0 ‘ :7 km (Va wag @ > :2.» i. ’ngo / w w ' b i 1 X3 E ' a S Wrdx J (QWQ/W%~> 2:5 E: 9‘50 O '6 X~€flgfi Cafiyexpnk 0 591;“...ng --c.-Mvw§mm, gnaé+.‘ H hm XMQD XL! XLI~L nh an... ) {m ,1 LV‘ } g:\\\"’7 12m” :: 1W“ Izfii' flu-5'6 (hen kwik WM 91%.? En. hut-i) 00 S \ ax x1. x“ .1400 3“ 1%“ WM {Mi-WWWWEH f gIC’L “X‘wy g . [thaw—JG) L flaw), 4.;- ‘50 44—35 \ m 9&5»? x?" ' "L 74- m M S gaff + Egg + ’72 mng 91: \n' IR “1.54%; km}; ’ '7“ "t W X ‘fwé ‘ L.D Wm, ng-m) fmwmg that ‘\ jig 3’: 3’ ' ‘i l. -- ole "5-1— Wham] .2. IL woéisem‘ .1 :65 n1 \ .L “Hug ‘ J Mimi-5 P ~42» ‘w-n+¢M/z CLWMW WM 6% 43;“ 4’ {1-35 afifi ANN ma‘fii Q (7% 4 fl" $5 Oi~§ if M“ m (34?!” C Wag M4» 93rd (:5 F'mmee.r of; Laéh iflpfifilfiw [email protected]{ ' .o Ham M“- ‘SWQM. inficmgi Cmvw-9§-_ GA hm: §ws~ L». k g x...» g g”. Way M» (9 1” FVMM \mAéx, gm Mafia“ 30 S QR {L4 Lu 4 x ink. 9’ s) L. 4_L_ X Ln“. 0w {M w 5 Léké S mi“ (1* 4’) xx )02K 1 L H 72.. IHIV‘ g J; AK fi‘m—a'm L gag-awn} 0&9 I ' 5:» 5 3; (ix ngpj 7319 Mgahfl‘j Z ' - Lgflm kw gNQrW Wme gaze zewgmg‘m § ...
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