ma305-06.pdf

ma305-06.pdf - l(a N Vxe CEOJ will sur xCDI > O HEW Clem N...

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Unformatted text preview: l (a) N‘ Vxe CEOJ], “will : su’r ’xC—DI >/ O HEW] Clem! N O H — w. o (t) = w o —_ o 3 ” may] I" ‘ HEM] “0L X" : Eu. leX)C+)|: nu}; ‘aLxCH’: ruin [04 Ith” +5 [an] t6 [cm] te [DH] .. incl g“? 'xC-t)‘ C [06.20) fELDll] = IMI """w 3:]; Let x73 5 C[0,1]_ 1'; £6 [0"], they, Ix“). s Sun? ‘KC+)! : Hutu” , awo‘ +éEDI'J [50:11 3 my I5“)! : "3"” , he Em] and J‘o 'xCD’ + lng—t)‘ é anm+ "all”. Hence; We 9 [on], lcx+37ml = [xcenjmls GCt7l+13CU| s uxlwnjuwj Ma 50 ””5"”: 3“? lex+39m| g “"|l,,.,+l)3nao. {GLOIIJ A; ”.Hm sad-.092; Nt’ NZ.) Ng’ H: aloha“ BL 11er on CE‘N‘]. I. (L) . Lineeszy 3 I? Luke CEo,I],+ke» I , ' Lam“) = f 2 xvii) (min) (tut: f 2x40 (hankmht O | = f' 2x40 Mi) At +f 2x°C£)L1Ct)At = LCLD + La“), 0 .0 E7; 1"]: Lg Cfofl] am:\ «.6 R ) £h¢h & n L{z><.-L) : f 2 x03.) (Quota At : fozxocnmeAt ' l —¢S 2x°(£)l~6t)d~t = acLCL). _ 0 50 L: C[0,l] -——>P $5 a “neav franJ—Cévma'kl.ovp COW'tD‘hMI‘g If 11 G CEOHJ’ fly» \LO‘)‘ : If: 2xb(¢)la(t)dtl é fl 2 lxbmHLmlAt 5 5‘2 lxbmlflkllwd’c é<§|21¥utt7lal‘C>\\LNM 11un- L c} a LaumJeJ "Wen-w 'l'YGlhlgavmn'kl'an rr-rom ‘ <CE0"] 3”."‘°) 47° C62 ”‘0, and JD '2: L: con'Uhuou. g. (c) . Let he C [o, q . The» ,_ I . l 7. 103+” -I(x°) : £1 (330(0) a“: - 5:, QOCOYGH = 5: [Cxefit)+loCt7)1-<xb(~ti) 141: I 1 ‘ l a. = 5; [ZxochCH + (kw) ]At : {a 2 refit) LCth + S; (Ma) At ; mm {0‘ (Murat cuLewz‘ L 1': 51: 'Ih ravt I'CLD- “v! V LG C[0,)] > I I s f lel‘at ~43: "Lug.” -_ "LII: [ICmU - ICXJ ~LCUI = { I:GCH)LAt L84; €>° ‘ CL‘°°" 8: 6‘ The" S > O 2 ‘3’“; V h 6‘ C [Oil] \{93 Sta-bfs‘c‘jiwj \lMla<8’ we have. VWS HM!” <$=e. nu“, So DICxa): L. ##W LCJ). Lei: "I 3": e C [01‘] QMA K 5 [9; ‘1. Then I 1. new» 0—00 x1) = § (Mm 1-0-26) um) on; ‘ 7. s f [9‘ C¥,Ct)) 4' ("“0 Qatar'] elf (using ‘Hae. Cows/exihj if, vaL/ : 0L 5, 6.3))1 0H? + 0—») gl QCZCthL At : Dbl—(*1) + Q‘”) ICE) . SO I i: Convex. 2.01) _ Lei: fife): et own) x16.) = e-txqf) , + € [01'] . U-S‘H‘ij bl"1- Cauchu ~Sckwa-r-L ,iheq’uah'bj , cue ok‘hq'nq 6: Cat)‘ M> <f' Q'tx’Cfl)2 4+) 7, (f' ee,e‘tx/ct> ow) 2‘) am :5 , CS: ezt a”) (Si: e-ze 6,“)? 4;) 7/ Q: ert) 491—: Q0) _ x0931: 0-5),: I. A5 flefl: d+ : ‘ —' (22"), H: £3”ch irked: .1 2. o z 91-: -2’f‘ .1 I 20,) If FCvgfiJ‘): e. ,5 , Jcken 10:): f FCth),x’Ct),Odt o -2? WL kave L : 0 AMA E = 26 la The EH)€*-Lma~r0\mje (ax g w'bom 2r 9F gage) xo’u-Lt -gL 9F xDCt) xgét3,'t)>=o V {- é a I up 9°C C > a” a} E . 1) and .00 we Lave. O -- i (2 2‘2‘: xc’Ct)) z o V£e[0,1] AL- Intefi—ratuhj, we. aloeqay, mm: cezh D, + e[o,.] Usma XDCO) : o amal x00) ; I we Lave. C+D : o Caz—H) =l Thu: CCCZ-D:l > and In C: _I_“ am} D: ~C: ‘4‘ (3—! 3 e1”! Consectueutij x502) : ._‘_.__ Celt-’0 '66 [o,l] . FToyn ICU.) 9 we Hen“; x know that m‘unim'lles I ____g. t 3(a). If F (RFC?) : to: P) 4:th 1(a) z I FCth), x’C’c),’°) c“: 0 We. have. (‘5‘: = o anal 9F 2‘. _s.”‘$ - The Eu‘ev ' LasqujL u tr n ; 9F , _ A 9F Dc 7, get); :o ee 6% q o J CX°Ct)’ x0 Ct) ,1.) :1 _9_F_ (x t X )> V [9):]. ‘3’"! JO «:2 0&5“; h 0 "‘ i <5"? C‘orct))> "-— 0 V 4" € [‘31,] I”+€3vfl‘t;nj , we 013%:an s‘h waft-H) : A, 4:” fume (”J-Lani A/ _ A! X: e CEO, '] ’ Art £11.25...” 4:th ' XOIC‘t) = A «Fa-c' J‘ome— Cbnfko‘nf‘ A - Hence XOC’t) = A'L +B 1 't6 [DH] 2 4‘0? fame A3BER. 3(5) Siflcg x0) b firee 1 41m +Yamenqlmj mna.'+,-°fi 8F Cgoce) ) xnrct)lt>J : o Sie'cl: -S‘|b (1:3)), :0 ‘Hqu'k {J —— +:| 7 ’ Zfi +::l —.s'm A :0. Thu; Aie {nfl)n62}, Mereover’ as 1600: O) we oL‘Ea‘un —H«q-t 3:0 _ The ch-b'cva‘ cuvve: “Ye. fls'ven L3 KOC‘k): final; 3' £€ [9,{1’ ‘n e Z 5-(C). A: "l S Co: 9 S‘ H: ‘FoHawS ‘U‘at ) II II Kidd’s s 16:) f'C°;erce)> Atéf‘ldt:l. O O 0 But ICZnflr-) : 5:." cos (2).”) At :: SI lo“: :I ) (the) O ICCZ n-H)5Y‘) = 5‘ Col (@n+»)5t) «Hz: Su~laH==——l ) O O 071:) JO Il't‘ ”floutawj ’tlant 1 Lu; 5‘ 3“,qu WMX‘Imqm af 4,0»). Wm F8303).- ’i (uhvfl) we) Kip»): an}; I (4:4, Lave, ICU): f F (XC*))uC£)Jt) (H; 7 90112.16 x U 'ch fo'uf‘or) +0 x/Ct3: JCCxce),ucH)) e e [0,11’ xc03=|, The Ham;H’on§an k amen. L3 H (aging) : FCEQAI) + 5\: $C§Jv§ = 1(3§2+v1)+ 03w), : sin? and 2H -_ «91-70% We alike-*3“: (av drug Jo 211 9% govern: n3 ”Una affirm :1, COY-‘t‘rd awe Sivan L3 ‘o/C‘t) : X,C+-)+ u°C£) Q11 Que), x°ct) ”loan-b) : —‘>°’(t) +e DJ] > '33 fl Clam, nahuom, t) :0 9w} ”‘J‘L’ "oC°)=‘ and yam) = o , that (s, XO’Ct) : xo Us) + acct) ~12 e I Fe/C'b) : - 3 Yoct) _ Fact) [0) 3) “a Ck) : ~15“) GuI'H') X°C°)= l) FOCI)=O . Hence we ok‘raiy) x0/(L’) .: ¥°C€) + H90?) : xocg) —- refit) E 6 [all] lac“ C” = —3 xccn - f6“) X,C°'):I rm) 3 fi. * ) 5‘ ' [KO-r0 I l —I x0 te Dan}, x000: I) 1 J [Pol] Lam—raj ‘3 “ _ h F007: 0. l —l I ‘L —3 —| J 41(2). W9. Han/e [Yo : e. [DU] fov some CQYIS'EHMU Obj) $/_ P0 F' f Jet l-I l = qua” .4; 112+ 3 2-H Hts: ’1 6 {11—2}. -1 E63 Cnve (:51; i J3 .4] I l " "I 12x l;-2' [-3 fl] [*2] : {—Z¥;] :5 ¥'—x’ : —2"l 3 3‘1: X‘- ' \ S.) V2.2 [3] IS an £‘3envec‘tflv rm. tke eiflznva‘ua ’2. Hm L; :1] = [-1 ;][:_:HJ, :11 m. ,0 r—~1 TX no L____'_) h H I I- u- 9‘" RN r—-——x On‘ OWN p d, 4' N no 0 u 3» :‘l LL—d l—~_.._I r———‘1 F—_"‘ m8 * L.—~.—l (5-) r-—1 ’cgg lu—‘J n I (9 fo r’ N 4’ 0‘ 0° r0 | n’ v N 'f 6’ b—s) r‘—-1 ‘0: 3 I‘___l As XOCo'): I “'4’? = I -a¢.&°‘+ Seafz cm) H Brae" : “Hart 1‘: HoCt) G714 YOC’DZO Luz, Luv; H 5.(Q)_ The reachable J‘u‘astare 9? x’cuz Axcn+Bucu ) 127,0) ad: iime ' T L: AC’rl‘nd a; 'Hae ref of a" x e [Rn p“ ml‘ich tide-re fixbb’ a Con‘trc' u e C[°,T} S‘uc" ant' f1 eCT—r.)A O X: BUCZDJC. O a O o O yeah—”ma er) , = I: a H t‘ L} = (I e «(2.) At) ['1 E JrGl'n [ ] o 0 ° 0 ConVevrelj ;£ x E gran, [I] ) finer. x z [06] A.» {cmg x E R a e o DC-flihe uct) -— & ct—T’ 179 [0,7]. The” LL € C[°;T] . Wt ‘1qu T CT—t)A _ _T 3‘1’ 0. Baffldt: [T T1 t a §.Cc)- Let v be q left en‘scnvccfor 0;: A - “Gr: 3 1. 532 Such fined. vA : 1v. Ufinj ‘lhductl'ovn I foe Jae; Hand VkeIN’ VAk:‘Xk\/. Since "Una we, Lave .raw‘t'e W. TOME [3‘ AB cJCJcr;Le_J 19:] C3) E A255 aA‘V’g] ‘33 ' A”"B] vi A13! 2 Viv-‘3] '. ~ $1“ij ‘2 6-Cu)_ Ben-nan“? EDUAQ'EI‘O"! if Giver. 103 9—"! (ht) + Mm EELOJ) {‘(mt) + Fcy,u,b)] :o ) Cxfi.) e @MJOJTL at we? "3;: 59 we have 1510.0.“ + m3” m Cir“) LL + x"... xlu'z] :2 C) Cth) 5 i2 x Co,D_ (ids) 9+. HER 9x 46(9). Let wows) : NPCt). "n12” 9115*”) = 4x3PCt). Let (50$qu (3: Lei: 3,": : B —a 82 Le 3W2” '53 3:4; (”3 = 9W Cx,+>u4 ”‘4+"1“1= 4x3 PCt)u.+ *4+ ”“1, ueE J 2x A Min-.mi‘ze'r 66655) 'Fov 3K)": CAM ‘oe ‘fou-nal auf cu k’IOWJ 2L3 h Cu): O Irg- 4x3 Pct) 1- 2:19.. : O . I Ci) . (in x’ II? (chlt):: ‘2X Pct) ) 'the‘n LL: CfofE) gqu‘s-firg: 6*) _ Mareavev) ) if ext ((3903:?) : 2‘2 7/ O and .16. (29091:) indeen‘ mfh3m‘uze5 31*. Thu: 21/ C’U't) + min 9X! (x,+)u+ X++ xlu‘ 9t ad? ‘3): _ q I .. _ q , - x 1’60 +1232 3‘,t(_u) - x PU) + 31,»: (69690) = Xq' PICE) - 4x4 QDCt))1 + X4 '—‘ x4, (P/Ch) - 4-CPCD)1+'> = x*(o7= o . ago W 3\ven Lu‘ W(7‘,t): X4PC'E) 3 fot) e {12 x [01'] ;_a-b‘r‘:fv 'HaL U' 15?.“M0tn/J €$MQ+“°“ (*x). M 1+ CO). Tke Grtima‘ control L40 is she» LJ Robb): #(XOCHHC), LeEO, T]) ”Lu” *0 'U a“ ““4““ ’5“ ‘0’“): Run, cngcqu; J‘é [0,Tj,xCo3=><1 \ ThuJ an oFUmq' Contra) Ho u ax‘ven L3 uocg) : — 2 x°Ct) PCe) ’ (z e [0"] ’ wLe-re xo 3‘ ‘1 rah-How {r0 xo’Ct) : uC+.) =- q» (1930”,?) : ~2x°ce) 'PC+)~) +£[OI'17 xCo)=l GCJ). F'YUY') Ban‘MH'H-f thee-(2m, we know khab T IC“:) = I F CxOCt) Moat), t) 0H: : WCKOCDDJ 0) A5 chgt): X?PC{.) cue kqve I W630), 0) = WCl30) 2 ’+PC°)= PCO) : 90 “-6-1, =__.L;E:____ ZOE—4+ e°) 20+€q> Thu; ICuo') — I'- 2-1, ...
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