Problem Set 1(Solution) - MRTBS‘Y 20:0 —20I( Winkr...

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Unformatted text preview: MRTBS‘Y 20:0 —20I( Winkr Sassccsni Soluhbns +o Pmbtcm Saw“ I. t (a) SHE L5 ‘1 $2. {cw-bi = [M (~le ‘5: {ml 4— ‘ «bl :— lal 4- Lb\. 5H6 (.2. “T8. Then: an MW“? ‘Wwve ‘Eweapuah'fi‘es +0 1>vaa hen .‘ cc) «blah; can JR? <5 155’ Z. til?) at?” g Tb Prove u“), but beam by mafian Wm} beam 05» avg 39 wt. ham: 2 a; '-‘~ q-q E- a-19=odn. Tb st? (fin) we mt Aé‘o 41: we find web é bflos 2b. "flaws. Cx'Vstvzb, whence. alt-19:130. 2. fime 1-0 Frau (if) we use He £04 Hxax Car—53" 290-, Indeeé, FF we cxPanJ 'H't lefl-lnard 33¢ of: 4N3. Nevin—(£77, m w +m a? *26123 +b2 7/ 0. Adding Limb +0 bo-l'h 9.32:. oé 'H‘E ineci’mh'ly yicHS fizz-flak:in 7x‘tmb- ' abserw. +ha+ +he. leP+-hand side. W5 61?, a. Therdam, (we): :7 am, 2 of)ka wt cam rearrange. as. C“__"$9 ;, ab. Again wecon {aka +03 aim mow" 01L (ad-H skies i1: 0‘chan “\WL desinu‘ {Ingmar}? : z ,7 /@+b\ 2: 4+5 V0.5 5 cf 2 ' Lb) SHE m fié‘k x‘ x a» p-mfclpom’f-o-F Pd”; ‘ M12: “1:2 ) 13%“) *vvu'éyofh? a( P3P? M23; Mia‘s 321's) 1 2 :- “PM A Plat : MN: (Egg , 5M}? L Nad’ use (2)um ‘fle slopes a? "He comm ex&g,: <3fl§),(3fi2) W» : 33’3‘ (—2" ) ~( ert (3fl%),(32+ a) .... 7* 2 __ 3%”3 1$a5q (xqu)_(xz—r)g " x‘rx l l m M cc.) awe b5 #66: Leat- Sbe W 'lcnfi-kho‘F one: of- +kcc43e$6§ Wedge. (9F) $civivx3 (2H 44» s yc‘ckLs "—"r 5:: Ed x/L ~ m meta 'er‘ +1»: voch SAW 6J3. Subsfihxfinfi ME. (ink; aim w; SHE as in: L% I; be Me lettng a! one 014 “Ht 5:323. fl: fiurZa/emf '1'"?ng , m! M h be flu herghf'af #9 maze-Mfg TN: parich 0-6 m vaimlozo is LS = 3K + 21a . $olvin3 flm‘; atmh'an {ny In wicks ts —s£ 1" ' 2 nu: ma 0? "Ht ecvm‘iafieraf #:hrale win fidelde ,6 (S ’7 ‘ A = E 2 T ‘1 (see we Eu?) TR: mm a? He nedanjwlar Far“!- 0? fit window is film by AB : bi = Z US’BE) . '2. meagre} Mbfil am a"; ‘Hv. mfndow If: given by ‘H’E Formula I A: AT z £08131) , 2 Z 3 .00 x4» 2x ~ 5X2+XK +12 £- 4x2. We beam b7 marmjmfi +hf5 {nefiuwfi St: 41W? 23‘ Mad; x‘fo— 2x3“- 4x2 + 53): +12 5 0 Now nohtc {M’r -(-'hc:. 169- séIe {50ml x43» 225— H2 + 32% 12 = Cm.) (panama) (Ont: may in flaw-c fins 00% (is {a 195+ mafia fha-f 'x=-( is on rooJr 04 Ht lefi hard sac: (."Hq «ac-13a w alt-132+ 9¢w1)+52. =10. Thfév means. W} (x-f-n fr, 4 {Enda- 0; #6 flefit 315‘ #3017 noquf “mg 'd'i'Vl‘sfon 31mg X4» zxg*?x2flx +l2— : (mm?— gxadéxflz). W6 may. on ‘an ‘fi‘élrvE sane L45 a:st 1'0 fem-(er '; 9&3 237(14): +12, 2 raw-3) ~ H Cx—&) = 012%) 0(3) = (X—z) CX+23CX'—$)v) Now we draw a char-(4 0(1 33h}. 1-0 dekrmrnc when: each a? ‘Hw W are Posfiive on mefla‘h‘w: "3 -1 2 3 wa) “ + Lxfl} " + H.412.) ~ J, tx-rDva-fiLXuMK—a} + " — + 7- .._ 4. 11m w {necyuauuw hows {or x 6 La, ~13 0 [2,33 . Cb) x+3 — 72. x4. Rearranfic 4M5 incapaaWY +0 W X+3> _ 2 >0 xal Now we, awufi 'Hae ltF-lr ham! 5134.: "iii. .- Z -.-., X+§ —2.Cx—:) L. a): ’ x-t x-t Tfifs mm; firm we Mani» f0 Salve m Mariya—UH? 5:5 K“! . Again “or draw a, chad, a? 6:39»; {o éck’rmmc what-ff: numcm’or MA 'Hc denominw’v/ are Posg‘fivc or- nfiqfi'vc: ?O. So “the ineimh'fi, Es W vabvfdccl xé- U,C).. (a) \ "S Xfl \4%. Recall ‘Hm—L ‘Hvu‘s ‘incctuatg‘fi 17s eim'valerfl ’m 3 _. .__*.. a 4 q “K x_‘ S , whim moans ’and' we wan-k ’tha values tag ‘36 ‘chl' 50.55%, 56% 5 3 HL£< Fag) MA ngéC} RflQWQ'fiinflg fies: 'ihcfirmahfits become 0<§jl“l and L"? (0, X‘! Wt how “wh’fi 4w; (3am.th Weaning n}, #25:: Meiaah'h‘qg.‘ fa wk 3 3 '— wan 3; 7"” x-t x-l i. ‘1 2:: 3 “WW-‘0 z. {m , Mex—~st x" X": X-“l x13 Our "hoo firtaLmla‘h'es how mac-1 o < 13 MA 3' (‘5 fix} x-: (O. We can make a, chari- o~€ flaws fir cad» o4 "H'af-c incimh‘n‘ahg: I ‘l‘ ' 4/3 (awe) " 3:? 1m» ‘25» 4w xe m) Thug M‘f‘fizfiéo {2W “(flog/0 X”! 2‘“! g ) U( a,m “is, mm Wed bo’dn "Encei’mlffi‘es art W '50P xe: ($4). R6160“ W4 +41% Maya“? Es efifufualcwfi' +0 The Fanw'c‘rj +050 {neat/M‘bffics: 2°“? 2/! 9.? ———--—- '1 m: 00H (med: 5% am sahkfi‘cg 'Hne m3th lnqm’lfl‘y FF and only if ‘1"? sah'za’éfes one 0% ‘Hnese +1.10 mew incciIuan‘es.) Eaarmrfiing m6 $€W1i3hfirmji The: Two Chaimlt'b‘es Mom: ' m 7/0 02 so. wfl "" wfi As umal , use now Make. a shark 56 gram; acer each of' W: inacl/uah‘fv‘esl '_ («D-H (gig) Luv—m Com—2 Thus, 8:? '90P X6 ("‘43-'91 c 00+! U (firm) New: w? aawW MMMg 0% m m? a"? fism 8305‘; 9% W WQEMF$ ggmgfi Ag:qu X413» W1, We comma M our Aon‘rdfa'ml immh'if ‘ g 'h-M '90P 'Kéé—OQ1*‘(1'U [~2,—:) U (4,60) . Ce) (X41 + lxwzk E z. “w” We. begin by newrffinj ‘Hqc (mac-Lug panch‘ms... x—L [-F xfll7/O xii x 7’! Ix-ll = ‘3 . "(x—n 1"? X”l (0 ‘-X “C X<l xwg («F x~2 7/0 x—z IRE X1722. [ME = "—’ ~Lx—2.) a? x-2<o 2-x {ac x<2. From 1N5 wt. 5:1: +hai “new: are +hm: cases {a wnaféer‘: Cage é) '- x< l Ca$¢®z (é. xcz [email protected] X772.— [email protected] xu. when xu we hair: hm! = I»): and lx—zl: 2*): L597“ ff x4], Mgr; xcz 41,503. THE means 11m" our ‘inectualfhf m4; Ct-x) + (2.-><.) .4. 2 <=+> awn s 2. => “2x 5». *l 6:) x ?7 3 Since. we mas-E 416:: have x<i , we wnalude Had my «heimlfi‘y {6 Wu: (:Or Xe [£10 Cascé)‘: stcz In his case use have [x-gl '= x-I and lxralr- zwx, and our original inctvmu‘? reacts (b04121) £- 1. 4:) IE 2. Thus. +hc Maw“? is flue fir a” X6: 012) Case 63: x 2'2 1 In Hat-5 case we haw: Original ingimb'fiv reads Ir)?“ 5" X“! awcl lxvz ‘ =9“ X*i. Our (,x—t)+~(x'2.) £2 £9 2.x-3 £2 <2) 2x $2 .57 (7:) x 5 Z_ Saba? we M50 Fatima x32 1%“ #113. case, out see ‘fhaf “Hm intiuah'l‘) 5% We wear x5 [2,35]. Finally}, we get +ha+ our original iwcobmlfily ITS: *m #22:“ Xé Ea, ’) UE‘IZ') U [avg/a3 = AS 2!; wit“ a. 25:4“ has? C33 2 n 1?? am! my P? 2% Emma) Cd) NOHCQ fid’ 'Funfih‘M Onty 0n ‘infcacfl yam '. 30m): 3(n+l+d) --- mm - [Vii-{+4} a “HM” 01ft) ‘11 751‘s Pnch 'Wd- use obEnin ‘Hm avapk sham ‘beiow. ‘- ,_ =3 (x1, 43-— do) Amwan +0 1% Mwbm 9g m We.th Ex} , wt "have Lug: k. 6?? cit/«é. M167 a"? ZXéfkfkfi), whemké We 65‘“ rewrflc Hus as M (It‘d in 6b) *‘ szlzk I}? and only (a? 2.5:: k-ea “3km keg m4 aéfo,£> “at? is; X= 5: + 5;: Med-W593 W‘E we; cm wnkfig jig-F again! ELK}: k 11" mfd only G? 'X: E +5 where kézam‘ bé Co, ‘9 E )9» gm, mH’h keZ w befioflz), my, Moo: was) :2 (gm—[2. gar-5)]: §+b~—k = "1'1? 415‘ (in PW¢MW, noh‘ag, +hacE if x= % {lop $0M ice—2, "Huen MK): “Xe? (A) Tb WAR +he absolodre. mane loom, we win on x and. a. Firs}, tack Had comm‘dep case's dag: xw and 3,?ro (QWmn-F I) CasaQE X46) aim-J 32/0 (Quadranl- Case.@: mo and g<o (Quadmm IE) Cage @: X‘avo QM (v.0 CQWJV‘AWE' 35’) Case (Di In fits. cam we haw, [x[+[.al.=. “43,: I! mkrcla signs 3&3 "X-H. Cm @1 Now we have, lxiz—x s9 =Lx1+1813 ~x+3, yieléivg s3: -x+(. @9369: Herc w'havz bxi=~xllkal=—3 so 'tatxl+tgt=~x—3, wm‘ck aims, ugg, ‘3 3“- “Xfit. £05269: In fifscmse vac-ham L‘al‘”‘3 ‘56 :lMHEE “#37 ‘Wh-Cdn :3in 3:» x—l. Lt‘ (a) N046 Hub-£- 031: a. meal b 493 ml numbefi, Hoe“ Lou-bf 3'0. ExPamAinfi “He. [69% 56:13 , but. have mz~aab+ 102‘ 2/0, wki‘dn can M be mama, 4:: W 062 +502 7/ 261.30 ‘ Zak: é a? +53 bLst’nj Ch b‘ a.“ 471$ 19: --~—--——- U“:2*a: W W68. 3 2 2 2m: za‘b‘ s 6: 1+ 19‘ l / 7. a ‘ 4f+4; \lbIZHD; 6“ ital, bl +52, b a: a2 mxd 14"" z dafwfi bf‘i-b: (A) From Cb) and Cc) wt have qubl S 4:2 + log \qu-mg' 512%: 45%;? bf +193, W < a: + b: .__._..__.\_’ m .__________ V/‘iizi'af «1,55%; “15*”; beefba. NS.” “#6” 11— kuoms. 1M4- 2gb + 2.4ng 4 a"? :2 a; 62. “av—1“““m —- an. 4 ——-~—~.. 4- 3 2. 2 . "pg"? '5‘" M“ We, obsem Wf ‘Hre. N8h+ side a? 4N5. 191%mte‘f7 Can he Smgtffimii 2 2 2 at + b‘ 4.2. b: 4?? a3 A"; Hf a 2 2 2 f a f— 3 ' a a + a ”’ 2 Q; “fag, h; 1““ ‘31 4; 1Lan bl 1" 55' al‘a 3“ “if 1‘63? TEE; gives. ZQ{b{ ‘l" ZQ‘Lb‘a “flu-'1 «diva? Q33. \J‘ b‘a't’é): éadcr 09 2: a‘b‘ i‘ azbz < __ [ Mam; Jbez‘i'b: Finally! we. MILWFL? bo‘fln 8:325. by \la-iz'i’q; \élbz‘2 +512 +0 $8.6; Won-E . I ._._.__.._I nge +3252; *4 JQIEW: Jbizfi’: I as. «Rama!» ...
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This note was uploaded on 10/13/2011 for the course MATHEMATIC MAT 137 taught by Professor Brainpigott during the Fall '10 term at University of Toronto- Toronto.

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Problem Set 1(Solution) - MRTBS‘Y 20:0 —20I( Winkr...

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