Assignment 4 solutions

Assignment 4 - Math 138 SOLUTIONS TO ASSIGNIVIENT 4 Page ’1 NM we to gtlnA 1k sO‘LLtL'OnS L $(‘3=o mun Lu-Q um%Ww WT“ pom‘hb-ns Weuak

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Unformatted text preview: Math 138 SOLUTIONS TO ASSIGNIVIENT 4 Page ’1 NM*, we to gtlnA 1k; sO‘LLtL'OnS L $(‘3=o mun Lu-Q. um %Ww WT“ pom‘hb-ns Weuak “*3 Point“ poem» i=ka 2:; met 41 mamfmua I (e. . on Intervals W11“). 50 gm (. 5(\)=O, m cm m wt“. Sn (LLO- cc>o , M 8,... 2.60.0 :0 ’ m DDWMQL. Aw 94-0- 049- x. <0 . NB. No sol'l‘ Cam powwoch xr-‘O E P34 - 2w shack ‘gpxc’cdl goutth to % = 25.; Hr cu SQope gfld . FUR»? oXmCuaYMI aka ‘8 “a , 36/2 =5 (j {Roaming .. 4%-2x-! “$20 ‘8 5> 1’21 (Cmswmd) 2 ‘ . 2 | 0%; < o ‘8 3 < JE— (CTMWM‘M) check 5: am: 15):”;— hams} 1+<saso\1‘, EBA-Hi QIth-é- ,Ma 24>ch = “gm-{Z- YES. 2 4 [5 o. speak? (waph‘wafl) Seaman. EVIath 138 SOLUTIONS TO ASSIGNMENT 4 Page 2 P54... 2e) Lon, wish To shriek Uépuhcd sokujfl'm , ch'r $0039 Max mm W sVMLXLi = (1503—0 (EV-2.). F1545? we. note WOC“ $.40 =5 (51—10 ,mBEha-aaaz {am emu-as SAD—L weddn 6‘50 {mm am am. 0-3435 «chm sowLé-ns. ‘3. 70 i; ‘6 > 2- M an, 04.3 <\ <0 its {55:014542. , Bride ‘5 fifth-ll. 1g (£15340) smug: F51 cg: CLM Hm“ C3933: 33-35:+25 =3> %’(8):3‘y‘_65+2 ‘ 3(3)”)- Iim 8‘31 ‘je=0: QCO3= 2 >0 =9- umST‘aML Act)“: NoTe bowfiu’: 39:4 ‘ g’c:)=—\<O w=t> MJfi‘Y‘. afiedfifixa we =_2- ; 93 21-“: _2_>_c> =_> mama aw” sketch- _{o_s4i¢a QEJY‘LJCLS flu DES an Mman (cit! mm} Mafia) .trv WMOXR C 053 = Acn-ecgfl. 5" % b obs )3Mfi—%=XCQSN =1: %=@.1fi+ D'ngo. fie, o, wa DE fl-Lfl boa c) ’K 0:37 = (396% 4.. ac (puma) = Coslnfi + x (2.052% =9 E: ASEQOSUECH'xh—zéra. girl’hho If3 °\% —_- Tom (36.41ng {S 09.1% Mm MPG-“M. N03 1 ampmédvxofi Jt'am Gui} -.: Mai 3 -.- MK 5053 *CDSX 5W8 60500”? Cosmcoaér—Smx‘simtj c3\oes no'lf W. I\/Iath 138 SOLUTIONS TO ASSIGNIVIENT 4 Page 3 P34 — #433 Ema Th9. m-eanmm 9% SOKLLl-CQAA 0% Wu a __ e‘sg'wf‘e 5‘9 (a 524:9 ‘5 QMLDQWQJXQMLDE %= 1:22.25. 13613420. Sapmaim% \IOJHOWi /% 1 Ag ‘ 635 Ch} 1 AQA’LG = [SW19ng (Hafiz €5>o Saudi 53 E a}; ‘ 3 19 “£3 , \3'AE LEFT-09'. -3 _ . (z W W3 £58 %&:jfle3&t=gm8wsBA9 ‘ , \___./ “‘1’ W :biP f0 A); ujxfl/x LA_=L:SJ o\\/= e—LISM _ _5 audit; ) V=~e'3 -_~ _.u6eLI—3+-Se 34.3 = “Be—3 _ej‘j_ Wngw “5e‘5_e_"j =3 {st-Jifi +Q) W38 _\_ ‘51 eflcfififi :fi 3 . C . Quota (thc’j Temsduj’méw {AA 1 l \ P$4v490 led. m (am-W % soiflw of MOE. §$x* r5: CosCe‘). m {J3 0. km” DE canal so we guhfi gJucL HM, wwdmg gQLFO‘l . 11cm: 85““ = et. mm H ice etofifi A. abutgr ~ éusfie’c) =1; 315%) = etmsCet) k to. . have» m to t an = getmceem TR'k \CV‘O == gees um.» L263 , ALL: ‘- " emu #C ecu. = AWCet)+C Math 138 SOLUTIONS TO ASSIGNMENT 4 Page 4 934-4:‘540 SaLue’fiu Id? ‘ Ecost+ \éSWd?=\, flCW/4)=+\E. swam a. a. M429» 05‘ M gqgox m Sad-m ILQ rgwfi. gm D‘KaMokcud gm M. TM DE Cm ta + w a - «at , w om mgwse—wosu =9 MWMDE L3 111:): Im a Ca $01.3 _.L_.. c - cost % +- 5.1m): nfi = 2% ‘ wft a) J... .. "t :21) 3%(cnst ‘ ML Lovl‘TD t: *C W1C $9-5‘W.f=§— ~19 i-hQJi)-;\+C pS4-*5€) Scum, m 5UP CH—chfa = b5, 5(0):} Qkabpka Walt-9.0 DE, 50 835$ hue, Mano-t; UMM-b-QAA: I : ‘L" Rt 33‘ H-xz MECCA/\afiufi were at '- c__ =6w\5\ = =cchanx+C VT TM Hm gamma} pohfihfiw Lb AMV-AJ: and-mm +C) ‘ an. “IQ: eam‘am'xi-C = KEMCTMX (KND' Wm‘fi the EC: 5C03=\ -=> H\ :KearLTam’D ‘- K wqu , Max: eonam’x Eyu’V' 5&9: =\ 70, U.)-°~ :3 )0 2 {0+le So\uilé'v~ MAM bl. Woman 3:2 lVIath 138 SOLUTIONS TO ASSIGNMENT 4 Page 5 PS4—93F5Vfi soku-e til/um IVP f-dii ~Lé= hast/hf 560:0 . , . . ax ‘ amtan fwd: Shun—A OE LL» o’t‘cmdgcmok (gum, M Jun-M 4'5 -an rta‘mjn’c, 600:0. auwm V 5': <t ' PM” 61“ Wuyatwci gchen u.» 119:6 b :6" 1*, l_ MDEMILV)S"EI so H5“ Lakes 1. _ ' ‘u 37'3""? t a} .. t1, - tam}: i,“ a. wfi‘to t- W M iCL/‘ZQ‘ tsm 0"" t - 1‘9 F ==3> 1tau“: :3 ~tcosf+ SCbStOUC :2 ~ tcos’r+ wafi' +C ‘ 5d“3 31> /g -: ntLQQS‘EA- t éuvxlt +C't IC Barbe» o = "Flat—Q +1r.o+mr (=9 c=_1r‘ WMSDP- CD 5: ‘tzcosth ts'm‘t «Wt. PSA~* EC) wk wl‘sk To Sghd. Wu. MfinocaonoJ. BachYmLm 58 flu. 5% two-DAG) may. ' weudk sah'nsflm DE. 36% -..’IA, Subce “‘9 “h?” W %=*% (Sm 11:03, me. bmouo Thu}: 861M mdxo%cnnod. “010.132.;th ,‘HM. DE will hp. 4’5 3‘- Cum'n Co = —- . Q 3 Pc "M 33‘ L5 ‘5 .L s-QoPe. ‘J/m) SQPMCL-xllmfi \IMS‘. “a (fag: Qanflcpahnck er0 K: j: £+C Z = z 2 1. _. M, 3—x=2c c,so..3. II I. 9% 5(0) -- “ {‘téh‘k/ng‘l' MOE: gao {Q x.=o v 54:0 41,3 15:0, «:0‘ w“ (umficod steps.) Math 138 SOLUTIONS TO ASSIGNIVIENT 4 Page 6 934d“: ca Use m Amfimnm M=3-x 1—0 QML MWOJL O'SMAOMK'OHS ca % = sm(3_><\ M‘g-‘K—‘b 0W=éfi~$=a %=%+‘=smu 9mm wavwgsmok DE {5 d“ _ bwu_\ . . ER ‘ 9 wexkckfi \S stwsaMm; \ d”. = \ (M# T—g—tQH‘W‘) ‘ . \o pimufi 5L? MLJX \V\ owxuud ' \ _ “9‘5 3 ‘2‘: mafia“ OALHS=D% 0% -\ Smflaéwofl/KACS UJJ‘. To x; g mdnum w = Sol/K ~cos‘u ==v SQ. Mafia;an __ M933 M 2 at + C m, _. Atcu —- TOM LL = X + C FwoJJwS, bad?~ ‘Vo néfixfl ~AecC3—fl —TamC3-q<\ = 1+ c: N‘owe; fiege arm thozle‘Al‘ Sokctu'uhs, \_ 012% w ( Procx ‘5’: 2 n ==X> % = \~n)‘i’n 53 ., go oXl— =1=n8§4d ’ 3‘7" 5 \-T\ on‘sc m M DE [5 2“ Q: + 900 2 = QCXX E“ 7 l-Y‘ ow =3 8" a + Q—flPc’d = $600”) => 9.13 + am) pm 3 = rm (1-10. whach .‘s a 9m DE so 900- m we AL?“ ’3: EFL-0 g a a (“a fi = Zzéf'i' “=4 S‘oounmeDE \‘5 x<€é§§=x¢+ 3%) 3L %,g%=2x r . . Jam x TCu. mfiwfin—ié {Sad—m 1:5 3:: e 8" e-(aQM\°‘\ = X4 > %\\)w\cS Ix —- 43x“ {3 = 29(‘5, tn (X’L93/ = 2°C?) M ma =-‘J<"+C =M3=- 9&0“ ' Math 138 SOLUTIONS TO ASSIGNIVIENT 4 Page Ex-h-ov (954-459 «TR; CQOJ'I'QLLJ" Ec‘uofi'ofi. g;- 905’— ergl)‘. (CHALLENGE) 0-3 To Show y : 347' {s a. SO‘u’fiév‘M ’L. LH'Szy = x , wax «as; x.2x-%(2x\‘=x" = ms ‘9) To Show 3 = Cx— {4C2 (5 0. so\v:'. y «‘43 = xc _J¥.c7‘ (5|.HCL 59C) v=x2 = 0.1— fiat: j :LHS. C3 The P320? Seems To final“ Izaak dez (s feinw-V is 5:17‘ , {ed-Hm. bcfiuffon 5-; X1 (s am‘enve,\ope’°% MM. €erS SoKufpe‘vxs 3:Cx-‘EC2. / ob new econ.) mm po'udr oglmmm'w x Q afi (5:)8 WOX L57: Cx—ficz. 3%“ 02 = -\ ‘ _ C _ ‘ C'Xa 7 [El («0 OI y=foiC2 WWW {usch 03' «a: c/Z, CU flack Poim‘k ,‘YW A9092, :23 L5 = x1 (s 2x°=QC/2-.-C. :: bQoPa ergTLq 9.11M 3 :Cx—‘Ac’: I ...
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This note was uploaded on 10/21/2010 for the course MATH 137 taught by Professor Speziale during the Fall '08 term at Waterloo.

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Assignment 4 - Math 138 SOLUTIONS TO ASSIGNIVIENT 4 Page ’1 NM we to gtlnA 1k sO‘LLtL'OnS L $(‘3=o mun Lu-Q um%Ww WT“ pom‘hb-ns Weuak

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