MTH 304 Notes, Spring 2019

CD 1.. 0 CcrmpAx tJLvYrvbel1/':L *" A ~ ~erz, ~ c1 ~~ ~:= /)L+1o \XI huuz- -rx.- I ~ 0JU2- ~ ~eJl./) am.d d; ~Lo' am ~~ ~0L- ~ ,c=-:1­ ~ * 1k ~ ri 1; ~ ~~ 1:3 I~J~Z~Q2.1 1JO:f)l..+1C1 '" 1k ~ at 1; ir, @~ ~(,3)= (iJ.r;o~ H( ....,~) 'J 19;>0 ~ ---rk ~ &b J V> ~ = x -~d ·-o¥---J~-+-x------7 X * 1k ~ font iii 6 h Reil) ~ QL J (}(o ¥ Ik ~ panlJ at ~ ~ Trn(a-)=~d- Exat"'f.~;; 5efuetR....~~ 5i+33+ 2 =0 6 ~ bZ - '-1 Cl c.. == :l.- 4-0 :::: - 3d. -::. 3li.-2­ - -h+JLS7-3 +1J31' 1J- - 20-... -:= 10 SOCIAL t J ~J::: • 2..J.­ ~.~= I . 0 L D?J J' "'- L h / ~ I .+ i AY~ 3' '" L ~ y +1-e C '}:= etJLoSc SOCIAL SOCIAL BeJtel"" -J'Y) e..thod ~ LV) l~ I +c~ LnJ~I-LY\c LI') J~J c· EX3mpJe. g 'Th:L. H1~SS (a ~e.. ~6L~ ab 0- ~ Pru7f~ f:;y Juts .~. J , _----/.-L K ~p~f1i1e. . 1:1 net) tP~ rnvvnd/& ~ I::~ g -\Z!!J ~ S~: 1'1(£) = c.e-kl; Hi'-!-f-- .' /11L H4-i!f- e{ a. ~I/e.~ if, tJk ~ 'Tme.e-cW h ~-tk~ te~· rl(T) = ~ 1'1(0) ~om!Ie.: TYuz.- nYLO/Y) (CL ~a.clive. ~ ak tk ~ 1:", c1j<"''< in D. zB ' Tb? /m-dJY) ~ ~ ~ b~ 2~ 00,Ob3-' (0-) F ,0-J ~ WJ-,.-t:bi ~ lb) F~ & h4-£f-.'T. ,~ -kc CL) H ( I) ::: O. z­ H :::.-k r I ·==::.D H ~ c- e­ (~S~) H(z) :::; o. oG t-1 ( I) ~ 0) 2-:=D C e.- K.::: O. Z- (I) ~ZK M (2-) =- 0 I Db :=:f/ e- e ~ o. 0 (; (z) ZK (2-) , ce.- D.O~ i -k ~ __- ;::. --()_e .= 0-, 3 c e-K 0, Z, 10' (I) ===D 0 .'3 C :::: 0 . 2. -=l/ [ c.. =2/3] » , I.... L SOCIAL b) T= 7 ! M (T) = l H{o) 2( )T , T "3 0.3 ::= 3 '==c> (0, 3) ~ .~ ::: 0,5 "T Ln 0,3 ::: Ln 0.5 ==f) T -= Ln0.S" Ln 0.3 PH-&b d. 1.. J-I W ( J 1-I 2 J ) ~ ~ 1~0'«1n: [) E: (j/" i(~:J) Let ~"''a(%) be a- ~ ~ ~ P('Lo/~J l1W- dare (~ ~ J p ~ ~ m := ~I Lp:= f(~/'j) LlP = t(rx" J~o) we. C£VY1 dwJij ~ P a ~ ~ at d8te. m ~ ~~- *lYuz- ~ !f ~ ~ ~ LD ~ Vk ~#4J 1tk o£ * 1h1o ~ ~ UJff1 be ~ fp ~ tJk-~e 8{~ "~ ~hlcoi,~ " I" ~ /Pl~,~<» " \, / \ ()PPJ'n./j-~ 1 ~ ) J /...... ( ~: ~ =. 0 r?L/~ =r;> !(rx-I;j) == rn ~I =- rY1 . ~ UuV/t. t ('X-/ zj) ~ 'm V:> ca2fLj I.s 0 c-/ l'n e-' ~ {A.rVJf,; ~tk..~( f~ :mth-~ tX/~ ~~ ~e- tk/.kv>n<- ~ m .~~ ft-L-0H > SOCIAL ~: DraW tk. ~ ~ t(tk- DE: :f=~-':(. ~ F~/V~/tk~ifn~~w~tfi.­ ~ a/7.11. 0t~ (~ ' d >0 G=I/ !ex1ij)? 0 d=t> zj- x ~o <1=f) ~ ?'xtt:-:t::) l \; ~ ~ ~ ~ Dvevv S{}mL at & ~ (~ aM- ~ bfhvip (J8Y ~ /)U/~ ~ ~) I( x1tJ) ~ m ==D 'a -x coo m 11- Y>1 =0 .' d':;Q( '* m= I / ~-= "Z-+/ II m:=.-I " ~=:'IX-I :I­ m:=: Z : ;g:::; x+z.. 1(­ m= -2. I ~:::.. tX-z. ¥­ m.:; '3 ; (; =:: ~+3 ¥­ YY) ~ - 3 J d:::::- 1):, ....3 SOCIAL ~ II I:k ~ '\1' 01 i:k £!u=' ::i'~ !C'(j) ,tJ-, 'tk. ~ OJT-R- £c~) z:- h'1 4==i> g::: ~ . IhJ2. ~ ~ ~ ~ II O~· T~ eI ~ I/~ fn 1'Yl,lXIendkt V~Jm-d' ~Xd 'tI' '" 4~ _2\3 DruJ-W ~ ~ ,~ . .~ (~f::: 0 ~> ~ ( 4 -(32-) ~ 0 -::=t/ j =0 J~::: 2-, (3=-z. (3 ~ ~ I < 0 d==D g(l.{ - ~2 ) <D (1;:::::{) ~ ( 2 -~) ( Z +~) < 0 2 ~ -co -z a 2­ 4- co ~ - - 6 + + -~ + .of­ + - +~ - cr .-f­ +­ + . d' + 0 - 0 + 0 - z /~/~ ~ ~~~\'8~\~~ ///: //// ._----+-- -------"'57' ox. ~\o\,~8\\~~ ////////// SOCIAL ® ~ /:epZ- Dt-=AX/!XhY1JL aJ·t:.lk ~ t('J )::=. rn ct==l> 4-~ - ::F= m * ~ =0 ===D h1 ==- 0 .:I- 8 :::; I --p /'Y).=:3 -71- d-=-J ===I:> m.:=-3 .:y- .--p h'1=-.o d= z k 2j ~ -2- .==D m==-o -;(- ~= 3 ===D m.::: -1'6' }{ ~:::-3 ===0 h1 == 15 ()1L-<L\X//JVI~ ~ ~ ~t:Jlw... ~ (kld S~) _--:~---\---\------\-----\--'f--\--+--+--+-\------\--yY).=. - 15 Sk~ S&me-f~~~~: (0.0) .rrl"'l ,..., \ , _ _ ... • ,. ­ I" SOCIAL ® ./ II ~ D,--wJ.)(/ ~ t tk. ~ t(!]l.,!j)'" h1 x. .x e -~::YYl =I:> d= e - m * m :=; -I )f IY)= 2 ¥- YY)::=. - 2 SOCIAL @ ---­ x x -1f" rYl =- 0 ->f m:::­ - I * m:::i-: SOCIAL @ 1.3 Sep~ D~cd ~ -I- A Is~ ~ [)£ v, r><Wl ifr be- /lR-f~ 'I'J Cvrl be. W~ vn ~ ~ t(~) J '= ex) dX . 7fLe- ~ ~ 'v> J/(/j)do=iJ(?G)dx J " Am ~~ v~ ~ CI V P) r6 if & fvm !d=!(x/tA) C){~) :::~ fX~ 5&tv~tk I vP . ;. ~I clnX -eJ -= 0 ofo) ~z. ~CtDx=Od ::::t:> ._1 d2] ~-Ldx (df~DE) d1)(.. ~ UYY')G SOCIAL @ SOCIAL T 1=k(T- TH ) =0 ~J" k (T-zS) air ~ kdt so/'~' T-Z5 j cJ T ~ Jk db ==t> Ln ( T-zC;-) ~ kt T-ZS T~Z5' = e.ke- -=1;> EZCJ-!-ce.kC ]. Kt ~ T(o).:: 100 ~ 2~+C ==-/CXJ ==0 c:='15 ===DT~ 25'+?t:;e . ~ I (z) ::::. -=t 3 ==0 ZCO + 1-';" d K;::. f 3 --:==[) 1~e2~ l/B ~ zK ~ '8 I~ B -:=. -::::;­ 1q zr; K e- J~~7 = i 0= T ~ Z5+f5(ef-;6' ==0j T=2-~+f5 (-f/J ~ t& a.- Ser~ DE TI ~ DE COM be- VU"Jttrm ~ ~ ~ ca'::c t( lJ ~ Ib C-arl\ be ~ to- 0- ~f~ O£ hOCY~ ~ ~1V~ a=! fxwrnr!= SOCIAL Prteb l,3 (z - I~) + (2.3; 2b; 25) 1-1\)(/ ( 4/ b / ~ I 23/ 26; Z'3) ~~ f~~11L -¥P~F~.~ * +Jeov~ 1-1etPz.cJ _2.._ _ 2... _ 2/2­ ~7-. n.. " J " I '? \ ~ + SOCIAL -' - I') di.1·~ J-I cJrx­ ( ~ ~+Z ~ ~ Lh r~} - Lh I(J +2- ) = Ln 3::- Cz.. :2. 1(. ~~ I ~ 3 ~2 +?(}­ @ :rVP: ~(I) =,2­ r * S~? 2x ~ ;~ ~ 3z12+~} :2 ~ dlj ~ (3i:J Z r >i?) ~ ( 'Yb ~ rrvi6 /Xf~) - 2-- t;t,~ {= :~ + 2~ ~; (~) 2 ~W~) == ! (!) -f L-eb 2;o~ =D ~ "" 'A:. ~ -4> ~ J + 'LJ{ J::: I 3 I d:l. I I ' q. 1- ?L. 3 = -;?; +- - :::::J/ Q::,. -!2...::- - 8- +- - . " () J_ 2- 2-3 J')L 2- 2.J SOCIAL ~z + ( :=: 5-x- . a./~ 5 2 @ rVP I t:l'-~I::: ~ + '" X an {W-x) I ~(Z.) ~O . !/r Tb Lo nt-e1; ~ '*' ~/:::: *+4~4cff,2(W'X) ItG ~ 'tL~r '31~!C'b) Tro ~ ~ a/v~; J::O~. ~ c::;. t.X-,3 =P ~/~ J +'X-'J/ . DE ~ b+ rx'2JI :::: J+ 4rx4 ~J­ / 4 2­ cxa- ~ li~ ClhJ' ~:::: /';X3 ~J­ dQ& 3 :.-f? -~J ::::Llx dx 0tLf~ j IJZ.C-Z,J d:J =:; Jlp:..~drx. =p tamJ- =. ?-4-+ C-. ! &vn ~) :::: 'X4~ SOCIAL I. ~ Exacl; DE ~~1hL~ (tzt~)~ d{:::: 1:cdt;r. -f- ~ d~ £x atrnt4: TI I"" 'Nz~ +I:/f ftn, dl ~ Ix d~ + 4d~ ;: (2.'L-2j)dx + (~2-J-4 21 3) ~ ~ It~C4=P dl=oj ~: ¥ 1= c =D Z£~O/ ,"=0 =p #000 " dl 0 Oo =P h~ Ie -(JO =p tumbc0.'T//J ~'t 'X- mm \3 =DiEJ :1 ~ TF..e- e.x.~ tU= P(xt't;)dx +Q(~t:A)el£1 v, rxUd w be ex.aJ- 11 CL f-~ 1tf)L1'j)~ -tb6 . J W = dJ J ~; TI w~PdlJL +Q..dg 0 exaa ~ Ip,t Ox-] ~ uJ e-x;euJ; =D W dJ 0= ,--0 PoIlJL +Q ~ '" h.d1<. ~ d;j =D p= 11L ~ Q. 00 ~ =P fJJ '" I'lt.~ l1/Y\oI Q'It = ~ '1'­ bd: ~ -= ~ 'X =D Pzr Gi.x SOCIAL @ Hetloct !:J.r ~e. : Pd'X +Q d(1 -=: 0 ( I ) ~st eooe-: A~ t:Ra.:b LV =PcJz. -I- Q ~ ~ exa.d =p j I /YVc=J/ DE. 1 C1J = 0 ==c> d!~o :::::p t= c S~:l!-LJ M ~ can.e- If LU in rneb excv:1 LXI~ ~~ tk 0 E b~ a.. 'f :=f (rx-/~) ~ tAa.h? lU ~ e.x ~)v)fL ~ d . /FtR- JJJ.JiJAr'o" f-;~ ~ == £:) (1)(,I ~) 'v) ~ CV1l T m.J;L~ T-'~". / ~~. gx~· saeve.. & DE: to d'-t- + ,~ x1~ =0 P Q Exa-J:: 7 ~ p=~ =[) Pij =1. J-==0 ~ 4Q~ ­ Q. ::= ~ -'X =D t:{~--, === D LV ~ tYU:Jb exa-c:t . * Hd% b~ Cl/r1 Lmb-~ fo-dm p"'p (~~) u drx- + ,f>(~-~)b· =0 p Q UJe.x.aeJ; =D Ptf =.Q~ -==Pt; ~ +r' =~ (2}-x)l-!'(-I) ~~ +¥ =~ (~-~) [~V,a.f~~ POE -jt S ifio- \X!e- m.e.e-J fYhe-. Vn~ ~ p SOCIAL \XIe- ~ t:e-H f =-f' (r:r.) &'L ? =-f(t£J x/-tk z ~ de-nJb lX/e'liC ~ CL ~~ be. c?f»~ fa­ r p *T~ r-=p(?L) e ~ = 0 e.vnJ h =f' (3) ~ 0 +7-f ~pJ(~_X) Itcaff/~ be ~eJ h~ U~ 2-V~'k,ld' -II'- T'O f;;.{fj) ~ ~ =-0 evn.d ~ =p' (3) =0 Jtj fl + Zf = 0 s o/?r:ruJt- ? ~ df := - 2-0 =c>.::le:> z.:b1 J o d~ r P d sit-==:. J-z~ .:;:=t/ LnL:=-zLn/LiI F ~ 0 K . L.n £.. =- L YI rO(Z=t> L:= I(Jr~ _, K K (jL =() p:= ~z SJnce.. V<I~ ~ i- tXI~ GOJYl t.aJ<e- k ~ I fO=~ -L. 0 dl)( .+ .--L ({;i - 'X ) dC{ :=:. 0 ~2. ~z () 0 I J ~-rx. d 'L)' - d ~ 1- z. ~:=. 0 (exate . . ( ·L l1 g J (Don't sl'mpl'fy It) uJ =0 \L c. :. ..1 jJ /: I I /1 SOCIAL (-? / I/o P amJ 10:= Q ~ ~ ~ p~ _, =p to:: J13- dx =V {=t + a(, ~ ), iJ ~w~ !7JU>f'edt::eroc. i~~+- CJ(~) D ~::o ;z- + ~f(d) ~ - IX- ()L bd ~ =- Q ~ ~2- 2 t ---w .'. 0I ( (1) :::t (~It ~ x) -::::::=D ~ (~) := Ln I ~ J + K =D {=;+Ln/~)+K SUnOL 1Ve. ~ 1! We. Cd/Y1 taJ<~ \( =0 t= ~ +Ln Ij1 ~ s~; I=c r; + Ln I~ I ~ c-] p~ (/-20) H\)(/ ( 1/ ~ I JI J ) Lt ) @ ! ( e-~ - ~ e-~) d Q + {Q e.,';1_ e~d:J =-D . Q f? *£xcul ? Pl1 - e)~ e')L I o - ".} ==-0 e ~ 0 /"I" ~ UJ lh e--xcul­ u­ SOCIAL I /'\ SOCIAL Q,+23 (":t-+~) 1 o ::;, fl ( t;t e + I) +? (,{, e + I .:=D p :::: -p . -D r ~ k'e:-'-'C (~Vn ~ 1-) Take. K-= { ==off -= e- Z] (I)=D (e,~-~ e:~) d'X. +(Q.ePH~-~)d~ =0 . *r {/ ell =-W t= Xe-~+23e--~· sef!u.l:L.m I:=.c. ~ .-Z, /' ==::::{;> ~ ~ +(J e. -=== L- . @ -3'(1dx +2-Xd~=O (I) I I L-.J P Q M~11& bOf =- ,PC QL/ dl -3~fd~+2?L'pd2j=o (2) uJ e.xoA :=D P~.::: Q-z; =0 -3f' -3C11j = 2f+ 2X/i.. -3 ~~ == t5r + 2?Lfi . T~: f' -; fCrx) =:D Rt copl evnd 11':::0 . o =. 5,0 +2 'A.-d =C> 2 Qt, df ~ _'Sf' .=v.Ee.:-c;d"" I I d~.? 2..~ ( In r I SOCIAL SOCIAL (,5 L~'hedY DE ~: A Is~ edm- D E. 'v> t>adl b be. L ~ 'iJ () ,;-, c{tJ...... ~ ~ [~l + (1.( x)~ -'= r-('k) ] ~ TlVz-~ ~ ba. tJk LDE tr,: I~=~ Jfvdx J ~ if = am ~ ~. e]a-C<>c)dxJ eaQa.J ~, t--1L,-ehf~ (I) b8 f =- f\~) : ~J + f:= f (2) Q ~ l flr u u Leh (' be ~ ~ tRai f~J +CLClf C=({''j) I (3) CL f Sl -+ a.. 'tJ f := f'~ -+-f(f =D O<-'8F -= f 8 ==C> 0. f -=-? / o...p; dp =c> Jp-= a.(oc)d<:<: =oJ.~-)a(Q:)d~. d~ p p Lh -- P- JQ(~)d~ ==D - f = e Ja.(fJ6)d';t . K K fa.. (tA:-) d~ We. ~ d P ~ Take k:= I =[;> P = e SOCIAL Bey nov II,' tguah'oh; 4' + Q (1:-) 4 ;: y(rx,) ~m -\X/~ m:4 0 o 0 t'Yl:t1 I :. a + a.(,x)a-=y-(-z-) I-m :=D ?JI + Q,(r;t)(I-h1)3-=- (1-01) r(x) L DE §~ S&Eve. ~) c- CL Y - hy 2 (w2Qd L~ rr::!!t::) o 0 (tJ<..lb)~omh. ~1 -Cl.-~ =-b t (6~) ~ 0ivLck.. 1,0 2JL -2 J -I I ~ d - a. ~ =-b Sc./;;n Z I - I- ~ -I ) -2 I -2.. I I ~ l-U {)::= (J ~ b -= -c1 ~ -D ~ ~ = - ~ ;. -i- a J- - b -D i +et-3 ." 1, (U~E) 0= ~' Jll-('>-),:),x Sa eJlt cvx. tJ~::I~ _ 0/)(.7 1rn~ ~ f=' e = e -= e =vr::-e. J 0L ~ 5~ ;, CO i-if rch -= e~,,-j ell. j, dry. SOCIAL @ ~. JeUQL)d<t J3rx.2-dO! 7..J2. +~c ~3 ¥ f~e:. =- e -:= e . ===D f::=' e 3 * S~: 2J c; 7-Jf' rcIrx. '" ~~3 Je'L £'Z~h ~ drx. '~.:: -'3 J~h OL ck, -=D o eX J Lj 3_ ~ (C8?h t;t, tC) o e'Z Ch'JpteY" :2 Second Ordey L DE 2.3 O~ 0f~ ~ Ii 2-~ cru:Lw DE !.D r:x:WJ bY be .~ f (j- ~ et ~ ~ :I~ 1/ -+ a (r;x.) ~ I + .b (IX) ~ = v(fA',) I (I ) 'Xt Y(~)::;o ~ ~/J + a('X)~ I + b(00)~ ~ 0 i0 ~ a. I-I~~ 1.- DE ~ (tJL D£)­ I\I~ IV It we ~ ~ I bS O~ cifYtc1 lilt bet D2..~ .tk.m D2~ + a..,(':\:,) 0:3 + 1, ('X) d = v(11'-) ( 1)2.+ CL 0 + b) 21 === v( ';t) Let L = D2 + a. D + b t9w" [L ((1) = r(fA',) ] (I I) 1l\wwm: ~ Of~ L- G0 i~ . 11uJ; h: I) L (~, 1- ~~ ) -: L CCd.) + L (~;L '> SOCIAL ~ '. L(Cli +-~) '" (.c{+ a.D +b) (~I +8z.) _ (~~'.+~:) 4- Cl (~/ + ~~ )+b{81+~~) ::: (~I/I + CL~~ -I- h.JJ) + «(j~ + a~~ -{- b2},) __ L ( ~( ) -/- L(~~ ) L- (tX~) := (D2 + 0.. D + 1) (0<.~ ) =- ~ d'l + a p(~/ +hoZ ~ = 0<. (~JJ+a~1 + b ~ )~D( L(~) D~ PtLBb 2.3 hJ 2; f 2- ._~ Hi-DE ~ : ~ &z~~ tiLDE', ~11+t.l(fX.)(1J+~'X)~=o(I) It :3 ~ 8 ClIlJ>.. 2 ~ t&- (i) ~ 02'-0 ~ 1 z ~<flt~ 1~, ctmd dZ ~ a.0>& a.. ~ ta- (t)­ 'I/ C j cJJYt-d C-z 0flY- ~ ~ Cj ~( + ~ 2:12- ~~ 0­ 2i~ cumb~ at~, /~2-- . p~ ~ ~, ~ a- ~ dJ (I) -D lfJ" + a(o:t.)Ll I + bcO(,)<.l = 0 ==DU~)~o '0 I 0, Of I ~~ if:> CL ~ af (I) ==D 1- (()~) = 0 . L (ci 23, + C 2- ~2-) ~ L (c.i ~I ) + L ( G2 Cd2 ) := C j L (J:j) + Cz L C~2) ::::: c/,o +cz,o-=o SOCIAL 1\)(/0 ~~ ~, amd ~2- evt.e.. ~ bs-he- .~ ck-p~ tt 3 :t ~ C j curu:J C2- ( rna:t bfilA 0) ~J\ t-f{pi J Ci ~ I + C2- ~ 2-'" oj ~: ~,amd~2- ~ ~ ~ ~I 1l- (~ ~2-)~~. ~~ ~t ~: xt ~,/{l2 ~ Ma-~~~69- ~ HLDE,' (ji)+ CL('X.)~I + 1xx.)~ =: b (I) ~ ~ ~. ~ ~ [ (j::C C, i:1( + C-z. 112.-] KrnBIXlJo 8, IuwU In ~ ~z ? Let cJ be CL ~ 1»- (I) ~ yl/ + a.~1 + 64= 0 0/ Ot I 0/ 'T'"'b t& fmJ 2.>d~ r{~ .juum tiz.=3 Q '1:'(?<-) 1 4 ~ :.-;j) 0 1J + a. U I + by :=: b (3) Oz. CJz., (Jz. Uz <.1 := 2:1 19- ==t> ~ I ~ ~ I '13- + U-'l9-i Oz; ( Z. I 0t . I j /1 ;.::[) U 1/ +- <..{ II tt9- + U /,,;r! + U ~ + d 119­ cJz. 0, o( 0, I SOCIAL Ln ~ + Ln ~12. :c; - fi-llX..) drx- ::::D Ln (~~l<") -= _f a(",-) &u I 2. (. L f))-- zjI - j a(1)(.. ) ux. I C - J'a-Crx.) dtx --:= e -==D f5l-.:;: e c ~~ if -:1:1 c..= 0 ~ vi=-o f> CJ:J-=cJ!.. =P )jz.::: f[T V, ~ =D ~I am.d?3z ClIL<- ~ ::J~ . ~ Tf c. c::FO =P 'l'!*0 =P ~ = 'I:T V, me/; ~ ill =0 :3/ 1~2 CltlsL ~ ~ekrem.kvti. r J(iK~ C ~I jJ) I J - fa(~)d~ j I-Ja{I)£,)b ~ ~ ru-..:: - e . 1? t"U~(?f..,).::. - e 0 j'X.... d{Z ~z . J 1 I -Ja(~}df)L ~Z" ~I 1)- .:=p 13z. =- 2j/ ~ e d-x. ~ If :J, u,a. ~~ w~ HI-DE: ~/) .+ aCrx) ZJ If b(x)g :; 0 ~ -tfk- .~&n La rz;-= -- f 1 - /0.(1)(0) eJl)L I 0t' C,il, + Cz. ';1;] ~ ~2-'::: 2j, iT e- a'lL ~x~: Se&e..ik- HLDE ljQ2i'+'BX~'+S=(J (x>o) J-Ifnt-: FWd 0- f~ ~ Bjtk.r 2l/=xln tf/ J trl-I . m-z­ ~::: t;t. ~ ~ = M ?0 =0 ~ II = m I /Yl - I) ~ 4J 2 (I) -=={;:/ )6 (M)(m_l)xm- z +cz?t. rnxm-l+xJ'Y)-=O. ==p 'X m [4 m (rtl. -,) + 21 rr) + I' := 0 ___~_~~- ±:JlJJ6~7~_ ""------"----_ b~1 SOCIAL I) F ('X'd}' ~/j) =- 0 Ccvr1 be. it ~O-- lSr ~ DE. b~ .' 3 ~ Cj =P dII ;. 81 =P F (IX = g/ /2- /'ji ::: 0 ~~ i j ~J F( f:}/ 8 ~ Ii) Co-tn be ~ -:=: 0 CJ=-~ } Unh& 0-. st 1 ~ DE ~ 121 d/=J p LA 1/ = '{.I c= d".. z J- ~ ~ & (1'-= J3' r-- o~_o ~d?L dO dx d i CF(~ /J- I j §' ~~~ £~ 2. I ( ( -- zz-) HIX/( ~ / J1" J ~ I Z 0 ) ~ 2 '2. _L..... ,',._rlt1J0. ) 7 ~ ~,-= CffJ ?L 1:3 ::: /;){I'""1 'Z (·cvr· {)l.. vrv- . 2 ~:: ud~ (p m6t ~ :c=Pt1j /& CW2-lvn. w,~. ~z SOCIAL -iTt ~~ 0 ==D ~/.::. 0 ~ [<a e-J . k 2 ~ d~ d ~ ~ _~'NHLtJo I -f d:1 =: - J /)//1121 =t> 11 =-- (>VYl ~ ~ ~ ~ f~ ~ J-~!j~ =P -t=W) j +GI =D '-t =: c.= .'j +G( =0 - ~ =UbCJ j.L( - d IX -:. (Cft>); +(.,) d~ /Xf~ f -dlX =-J(UP» -J-c,)d:3 =f) [- X =: ~ ~ -I- G, g 1- C Z_) 2..) II I @ ( 1 d - 2XC3 + 2.c8 -= 0 2-2- -?t t/I Zrx.. / z.. o - 1_ 7tZ ~ -+ J _ x"Z d ~ 0 L DE. _~: Vmfo -fflo1 ~l =- ~ if, a- ~ d==- 'X .~ 2J 1= I -0 ~ 1/ = 0 . [I):::./) 0 - 2x ( J) +zX::=-o e----­ If r l p--- f Q ex)~-:( r I d?- -= lj, _r SOCIAL ~ :::) -- ~ dl-- 2- J 1 Dbc A ;xL ((~;X) f~ f'~~)-f~~ Y ) - I -~ ;Z'1((--;LJ ~ -X'1I-X) C1+1-) -I- J: ~~~~ ~~ * D)I)-I tX:2-~ ~-~vd ~ (a~o) :1) It 'tL., f&X/erv> B/t7l- OJ/.£.. eA!em We U X= 'Xz..,;, tIL.. ~ , I __ _ I == -L + __'_ ~Z(I -'1Y) )((I - ~) X t - X ::: ~ + .J- =- .J- +-'--­ 'Xz. I _1<-2 1';0~ (l-7<.)U+x,) SOCIAL 2.2 2~~ HL-Of:- wJi ~ ~ ~ t:9t.... 2ru:J~ I-IL-D£C.: [~JI+CL2(+biJ~Ol(l) \X/~ a.. cw.d b CV7.JL ~ AIX ptfrd CLF~ ~ e1~~ St=e ,,'1:. J \ Ajt I) \.C. ~ 'X. ~.:: e ==t:' d::; ",e ==t) ~ = 1\ e AeArx-+ ~ ~ (I) ,. 'A 2 2'r:k.+ 0. betx-==. 0 ( >-z. + C<.. >. + b) e!'~ =0 =C> 1r--:X--:::z.:---+-o..-~-+-1-::;:-0---'1 ('2:) I (2-) ~ c.oQ(kd .~ I ~. II \ io (h rcoot W- (2) ~ ~/'" e>-''X.v,{h ~ bY{/) .t'CiJnP- It 6 =cl--it), >0 'IYuun (z) ha.0 2-~~ twtif;; PI ¥}. 2.7=D 13, ~ e A, 'X.w=1 ~2-"'" 1'2-"'- afU2.. Z. ~ ~~ eX,'X.", e.(>..,->'Z)?<-0 rrwC ~ b~ A, :f.t-z ~ z. e>-7. 'X­ -:::v LJ I / ij2. 0/tsL ~~ t/tldar~- ~ .S~tiEYn '. ~ -= G, ~( + c z-~z . ).., ?L Az. IX, C, ~ + Cz e. SOCIAL n.. ._ t7. , . Ai st. )., I)(.. ~5~ ~:;::Clzjl+CZ~2-; C,e +CZr;z..,e [ d~ (~ 1-(.2'1<. ) t!''X./ 3rd,.... ,...0 '. • jJ _-+ \. VUJ~ T b b <0 .t9ttm (2) b 2- ~ ~'. \~=o(j;15 -==C> 0; :0 e:' r.t.cvnd }Z-=. e!'?- 'X cJJU. Z ~ 1(3 *g h~ -f-~I?~A aJL<z.. ~ ~(~ ~elj{L~ ~-ZJ ex~~) ~ ~ ~Uun he,~l ~ .~" %'1 =- e!" Z e(tXt-.«3)?<-_ e rX.?<- +--'th: r!"'-(tff{5':L +,c~f3')0) ;>"z...~ o(fJ<. -.tf5x- o<.q. ( .). ~z := e -= e ;:: e ~fBrx..- - i f)l/Y) (3 'X @ =0 ~~ '1Z~ Coab&-t7~&{j) X ~, +~ :::: 2 ec<..'X..cm(3"A.. =D --t ~, + -t h. =- e,rX..'X-cft>f3?L {/-, 0. ~ ~ at'J( amdJz =P 13 '" elX~jjtL t-o,a. ~~ 1 1f ~ --~ -= zl eP(~arx =D ~ _ '32. _ rJCXfX.. ~ (3 I _. _ _ J-() (II ­ 0/ tJ '& r ~ -, - ~ /Xn1 Q L.O UI>'U1l..11JV\ .J()J). . 2,( Jt-<.­ esmb. ==I) dz;"e~~p0t ~~ ~~. * ~=- ~f3~ t-, ~ ~b~ fJ-F b =f)~{/»z-~:!i.r" ~Jud ~ ~ '" C-':J I + C z 'J2­ 123~ etX'X.. (c, (ff)(3Q +Cz~ f3~ · SOCIAL @ © ~'+L({+5d HL[)Ec. =0 ~. ecru ).,z + 2 A +5 ",0 .2 ~:/.::. l'2 - a...c. :::-- I - 5" ::=- - It =l; L f,::: -:.11=JtJ:::: 0< + )'..;9 -I ±2{ '=­ tt. I 0('2 . ~.5t1. d::; e (C1C&:>(d'X -f C2 My2'X) 0::; e-'X (c, Cfu2~-+ Cz oi., 2 ':l) SOCIAL SOCIAL r~ p~ l dlo ) =~ ;:::{> cJ=~o ~ :=\? ~ :: ~D Uh LV t + Cz /Y.rf\ 4lt T~ V~: ~J(o)z; fl{; ~(i)~-~ uJ rxinuJt +cz wabw-l; o ~ ,==D ~/(O):=; CL W.z 1% ::=p e.g. = ~ p~ B/ m al ~ (;, 23(c)~ ~~l.Ut -+ ~ .",;", cUi . S ' ~. r' I A h'l{)JY) cf h1 keJ ~~O(.. ~~' ~/->m~. ht Ii1 riz r 1<1. )( Ab ~ er-£{.b~ f~/ ilk- j)Wm CJ/ aQk!., ~ 0 o. ~ ~ ~ w ~i*J 0 J, '" m8 . 1M j<n-'-"- r tflu-- ~ O'YI 1Y1 :n : J:..= - k 6.L (/-I~<h LaW) 6L:= h -==0 g~ -b, " + J =P VYl3 - k;> = =p [ k- ~'iLJ 0 0 z fxary4. A ,baiR.. t( W~ w- m~ =3:3 N.wbsrv> .~o.. sf~ o. I meiM.... 0-) F'thu:J tk.. Sf~ ~ k. b) \X/e f'~ dwrIm ~ baiQ am CLdJ~lt~ (). 15 Vn ~ ~ J- \X/~ Q/tl .~ v'~ ttJQ -=: D-35J67 mjpec I F<in.d ~ ~ (~M!l, C) FVd til..- f rv0Jd T c;r,-r.J tk.. ~C:J ! ~~--------'==--=----------- SOCIAL ~ .:: Ct U<n i iJZ6 + C2- nw, =+J2{; /) ~ I", - 1JZ:e,'*"1tf2h lficz/>i"wt/: * ~ (0) '::: O. I ro ==t;> c,:;; O. 's­ *" L~/( 0) ==. o. 35'" J7=p 1-JZ Cz :=: O. 35 V?' :::0 (.2- := o,o'[;&' [d':: 0,15 L£YJ1tE& +- 0,05' J3' ~ 1J"it, I 51 1M- p~ T VJ ~ ~ mewlad t&-~h -1~ ['G ~ 1 c>1''''::] Tk ~ 0 til.<. ~en( ~ f07.- ~ I~ 7T,~ i > 1 ~ /r---g=-+-~-I -=t>!! = ~ ~] PrWb 2. 4 J-I- W ( /1/ 2~j ,LL)I 5") SOCIAL z,e; £~_ ~ £~ftT1 ifi..L 2~d~ (;~-("~ ~ iD<f&pum I-:i'-(j }j + tl 'X. ~ I -t- b21 '" 0 1- \XIlw-<.<- CL and b (;lJU1... ~. IhW iDlL L.-Dr: but t:R..- ~ aC'X)= ~ ,b<oc)~~~ d.Sf rnelkd;; rtft,J 0- p~ .~ at ~ ~ Gt= ~ GIn z.hdc;rukrt CJ ar>d Mil ~J.. rn I m-/.I m-2. . ":J''JJ'l. tJUJJU\ i.{:= fX. -p U ~ vn X ..==:/? U == )7) ( h1.- J) OC 0t.LL~~. <J 0 0 (I) =D Tn (Yn- I ) rx.rn + (A. h/'/LYY) + b '2rr)= 0 ::::;;-D IT)Z _ j71 + Cl. Wl +-b .::: 0 =p {rn" +(0- -I)::;;:r; =0 7(2) II h'1 in Q. ~ fa. (2) .~ 'X-h'1?:,Q ~ ttrCi) *" rf 6>e>·~(z) k 2~~~m'lm2 ;V ~ 1:0 ~m j ~ ~t ';t, I'Ylz alV2- z..Q,;." ~, ~. I'r-.~ _ r _IJ Yl'Ij Ynz lX/Il . dB( : ~.::. C t f)L + Co2 f)6 )i. T t l:J:= 0 ~ (2-) Jruv> a.. ~ ~ m J":::. iYJ-z -::::D ~,:::; 'X-m, ~ CA.. .~b(i) .. . n4 _/1--H ~ . J I -J~ (~) d?<. 2 S~'" 212-= ~( -2- e d~ ~( &m, Sri! 6:0 C I I)l/"\- Cz '62­ If xl !J <,0 ~ (2) han 2 ~ ~ :;~:o IXi' ;til' . ~ ~ j = 'X>mI at>'U:i ~z. =~mZ. arvL Z ~~ W- (I) kJ­ '" 11 , .I ­ SOCIAL SOCIAL LeJJ /t,L/::: eb ==p ~ +Z~ + ~=o +lLD£ C­ * ~. etju Az.. + z ~ + I=-O -==0 A I :::. "'~:=; -I ~ ;;. (c( +cz,t )e.-6 =D CJ = (c, +-cz- LV! JXI) l-xrl . (" Cz- Ln I~I ~.= ItX.-/ + I?d ~ ~I~ 8z, anR- ~ ~., W=o ~ ~I '~2- .~ ~ <1=P t;G(j;::p~?-C~1 \XI ~ ~ t ~ ~ - ~2- ~ I' :=: dI ( C. ~ Ii) - (C ~I) ~/ .=;; 0 . PrWb 2, {, (J - J 1-) H'XI ( 1-/ j / )3J 11-) 3.4?t -2S7L (() j/ = e i ~z,=e -z9x. -2se a..) L/Yl. def.? 3.1.( 'X. e" SOCIAL ~ P'v.J a. LDE: wlw>e- ~ = g,t~2. ~I t ~z. cu-az- ~ fD- Vh. HL DEC lX/iw= ~. ~ b2~ ~~ "',-=3,4 / Az.-=-2.S cLn.. er-: (>. - ),./ ) (A- >-z ) = 0 :==D (>-. -3. l( ) (>-+ 2.SJ~ Q 2. '-==0 A"- o.3A - 2?/5"' ~ tJ . LDE: I'aN - 0 .3~ '- 2S21 =0I L_~i"") .. i) SOCIAL ~.~; (~-AI)(A-Az)ZD ( \ + I +i) ( ~+ J _ i ) ::; 0 .. -e> (>-. + 1)2_.-<-2 -== 0 =P >? -+Z A +1 + 1 =-0 =p 'A 2 .,.. Z>- -I- 2 ==D 1-Df: ~ of- f~ +2.~ ." a . o.-i~ ('_ • .r~n.. Z- JI Q.~3 J ~6~: rx ~ + 3tz~ +2~ =-0 2.'1 Nonhomofj€ .he.oUS LDE­ '~ I ~ ~-iYuz.- !-De. ~ ~/I+ a(x):cl' + l(rx)~ == vex) (I) Lei ~h be -&- ~ IJJ- tt-H L-D£,' ~JI+ a.(x)~ '+ b(z)j =0 (2.) Leh ~f be .be. Q ~~bJ.(I),t1m ~~ ~ f:cr (I) ~ ~::: i3h -t ~p RriJ8g,. V j.=: ~h + ~p if.> a.. ~ br (I) 7 L(21) -= y(~) ? ~h 0 Ct- ..d. 1::& (2) ==[) L~h)~O ~p {p 0- d. I:a-(I) =c::P U~f') ~ Y(x) L(~) := L ( ~h +~~) -= L( ~h) + L (~f)=- 0 + y-(~) -==D iJ ~ ()., a. ta- (t ) 1 :J,) Ao~ t&(O Lo~tAa-rm /:j=:Jh -t~i . Leb ~ be, O-~ t:trCt) ~.D L~)::: v(;t) Z3, ir, 0.. ~. 6a-(I) =c> U,)jf) :-> Y'(-x.) ==D L C~) - L ((Jp) '::: Y - y -==17 L (;j - ~f ) -::; 0 =0 d ~p VJ 0. /Xi - 6-(z') . SOCIAL g)(~ I ~" + q~ '" 1)0 (I) 1-10 m ~U : ~" + 4~ "'0 (2) I1L D£ C \2 :z. '2. ~I +2.' ... 1\ -+ 4::; 0 ===c>;\ ~ - '-f -== l.t A., ===C> ~z. ~ - A. '=-0( !;13 ~h:= eO 'X.( c, ~ 2·X -r Czd"llZ'z) [ ~h '" c/ CBY2.?L +Gz ~ 2XI Pani;;. sdl. (G-ue ss ~f) 4~ =~ =I>/iJ '" 7; )=oj> j' ~ t =Pbl'=-O1 ~ Vn (I) o+4(~)= 'L V [~f=f] G&n. SoI d=d3h -+::J -=t> l~~-':::'-C-(-C£b-2-'X-'F-C-2--.~~'-Z~--f-v'l p c~z. '):,2-~JI @~~/ +2~ '" rx--lt (I) a-=- -2 IIDm. S:,l: Q,Z-:;j" _ 2'Z ~'+22 '='0 (2.) ~ L-ee (?L ( :: eC~ ·t =: Lv> (x I -I? gf}~ +2.(1 = 0 1-1 LO£ C 0--1 ~ -3 l' c.9zan. ~: )..2._ 3). +2 :::: 0 .:::::i/ >--1 =I I ).Z. '" z.. '. /.. t >... t t . zt « S oe ~ .:: K, e' +-I<z. e ~ =P ~ =KI e + K:z e l:J= K,lxj + kz/'Z/z= €§yx. +~~2 C. Cz. [-~-h-= -c.-,~-+-C-2-----:?-~r D 1 C IJ --../J ... ~/ J SOCIAL .-6 " _J, 1-5" v(Ji ZOa.. x.. r< +IS =r£1.f .::::;p ~:::: 0... X '-f -==D ~ -= - 40.. XJ -=9 (j =­ ~ Un (I): z. Oa.. ti: it + 25C\. <;i:4+ ZA ~-4 = ~- 4 =0 30a. '" { =C> a. =~ =I~-=-~-~--4---'] ('- ~ S { \( - Z- - 4/ L>VJ1. ~. _d- c, x -f Cz X -+ ~ 'X­ 3 Y'd~ -k>- obfa;.,. ~f i Uh det-e~ l'Yllne-d Coef,frclenrS He-rho~ " ~ tJk LDE : ~I/ + a.~/ + htj ~ V(Ql.) ( I) whm..a- CL omd b arr.e.. ~ ­ Let !:J~ ~ CI~I + Ce~z- k ~ ~ b-~ ~LDEL . d -fad I -+ ~a ::=: 0(2.) :lA~m1L blctl- ~(~) b frM- E(~,~~ ~: l2!fe i: r(rx.,) == ~(~) =- ao -+ ct(?<. + . ,,1- cth xniho. p~ at dar n. Tdfe 2-! r(x):::: etXlX. ~ (x) T,!1'''- 3: r (X) = e..>'-?<- [Pn (CL) CD:>(?'X. + Qh(<x-) ~'X-J W~ n~ Max rck~(pY)) ~ ~ (Qt))J --rFiMJ (I) b a ~~ t>b.tk.. ~ Of'" Qh1::J(~) \XJhuuz.- ?J (?v) ha.t> ~ ~ ~ t:t/:) ("(x) anc1 m io'~~'k nBY/7Lv r e- ~. ~ &l- 2j ::~~t?0) ~cL ~ ~ 1~~-tkJ-aJU2.'P~~b(2-) .. ~I (oj" -2-2(-:::0 xl. (I) W.A1'1L~' 1. 11 '7 ..• 1 ~ 1 ... '\ 111""'­ SOCIAL pdJ.J;. S8f.,! 15r~ ~ (}f : - z~ J;;I;t2. =c> !'J '.:: .::.t :=D ~"==-'X. (I) ==0 (-7<.) - 2 (- ;L) =. fL2. x· X Zhdme1fiocJ L I-J S Ii:> ~ a. ~~. 3rJ~ U~u1.:.ct=-z./b:::o m=~. y(~) == /X ~ ~C?(.) (TYF I) •.• (i) h.v, 0- f'~~ ri ~~ j ~~fz(?<j ~ ::- I)<-I'fl ( 0. I;t2..+ k +c) ~ rn FO b~ ~=a.¢+bx+c v,~ ~ ~~ 6f! ~ 2, X and '/ c.vn.J i (./:) tl. ~ -!:b-(Z) *lm -= Ij b~ ·x~. /)(.2~ X ClfV2. m-eb ~fu{2) ~ =- OJ}/,3 + h?f+ c 'X. =I;::> gJ -= 3a-~2-t--2 b?l t-C ,=p dil :::. , a rx + 2 b. ~ v" (I) " l'bQQ+Zb)- 2(30. o:.-z-i-2b~ -f-G):::'-:z,z utat t;t.2:. - bet:=. { :=:0 a.. = - ~ ce18t ~ ~ £Q-i;Lo =0 b -_~:::--It ~ . Zb - 2G::::: 0 .::=1;> C -h -= -~I 'f ~p _- _L'""lf"3 _ J ,.." z. 1 0, t '4 'V -II 'JL A.­ SOCIAL z~ 2~ ~ ~ ~ a. r:x.- e .=={) C1 J -;. 0... ~ ..f za. ~ e:; 2,,~ 2fX.. Vx. (J). z.n,. :::::;D~'I::, Za-e.. + la- e + ltCl/)l_e, ::: l.(a.e: +~a.'Xe 'Lx '/../11.. . fft.. '2/2#.) 2,'2­ tI) -p ([{tA. e + ILia/x. e, ) - z( ae.. +~a '1t e. I ;. e.­ m e~ / :::=[) 2 a e :;:; ~~D Za...=. I ==1/ ct.:::: z / ~f ~ -t X e- 2'7 G&n. So /. l 3 ~ C, -f C2-e?"'-+ -t- Q. e2-"'-1 5 UrYl Rul e (py-t'I'1Gie!~ _t>J Supe-rpost't/or) Let ~p. be. CL-~ ~ f» OJt+b.(x)~'+b(x)~ =~(",) 'JPz. be-a pwJ;. Sol !:fr ~J'+a,(x)81+b(x)1J::; Yz.-(x) 'Thv" ~ := ~R + j ~ (L pnI. Sol br f ( & II J ~ + a(2) ~ -+ b<~) ij =- r; (x) -+ r~ (1](,) () () .. ~ . SOCIAL @ -x,'2~ Ii- Z-~ ~ I + 2. tI .::,[/ +J'?l ' (j) ~z~ "._ ?<.. zj' +- ~ .::: Ln (?6) ® <:C t - z~ :: 01.-+ R (I) /-10m. Sol. ~2-~" - 2.(3::: 0 (2.) ~c.Ib a ~ 0/ 6= -z. Lei t~1 ~ e b -p t == Lrd~l j i i -zd' ::: 0 H L-DEC et-i-=--I '\2. _ ~ _2 .::: 0 =P A{::: - I ~2.. ;;:: J. I ._ k -t zt z + )( .z. ~ - j e + K2 e :::. k',} rx.) :=; - -L4- !<2 x h ~ C, 2.­ dh ~ Ii"" .+ Cg ~ f~. Sol. " 27.)4"- Z)\::: rX. (3) SOCIAL r:>t'!JJ/ _ Z~ -::-- G' (l.t) R/-IS -== J;:' .~ d,f2. 'T~ fb r a. pe/!. i tAo- pum C1:= 0. rx'h­ ~' "' +a. r£YQ.. ~ ';1'1;> - -q- CL ri' 3/2.. (4) =1/ fa. iX-\-t2 - 2Cl. r,t,l<l. "' fX"ye- -=P -l a. => I ~ a. ~-~ [~ t{' --} .1>-] (po. fcu-J,. neE. b:r (If) f?q .~ /')Urn') Rulk.-: t-\::; t1 4- (,{ ~ - 3:- - JL ~ o 0 f F; 0{2. 2-:) Gun .s'ot. ~:::- gh+gp Cj 2!Z... I, Q d;: .---;;;: - 2- ~ + C-z. X - V% fbnl, SoL (u~'\de f. Cret.) rex) '" 2 oX ~ ~ '" e,0X( p,CO:>':X. + QI~ -x.) Type 3 (I) b ?L ponJ:,. rxR. 1 tR.-~ d::: IXIn ~ ( IX)::: QLm r0-1)(. +lVun()(. + (ox. + d )~.,;;) . I . SOCIAL -- ------ ® ~::: (aOG+b)C8JQ<. +(c,z+d)~QL ~).:::: a- CBJ rx. .- (CVX +b) nhJ?t .f>G t::>&J QL -f' (G x -td) Lib x . 2jll~ _2 (.L ~ 'X. .- (a c;u. b) C8JX +- 2c. Qb~ - (c. 'X -I- oj) ~ IX. I [1) ==C' - 2a. ~?( - (a x~ (X, + 2 C CB::>Q( _ (CX~~ 9G -I- 2q ctP~ -- 2 (~~-rh)~ rx, + 2c ~ 'X-t- z(c,~·+d)c»;)x +( a ?t~c.m~ + (ex~~ Q := 2x ~Yl ct &../. ~ ~ Cf:brx : 2.C -::: 0 --0 c = 0 caf· 0/ IX. ~ ~ -2ct ~ ==D i : 2- a,::: .... of'1 " 2C-+2a+zJ~o:==od-= [.£r>X euf··ct : -2<>.. - -z-b + 2G:::.o =0 J,.= I ~ 'X. [ck= (-~ +/ ) CtbiJ:, + t?0,?L] z G&n. Sol: l ~ ~ (Ct + Cz -::t.) e- + (I - ';t)CR>~ +- oW, 'X j @ Tv p; ~/I - 2(\/.; /zl-"-- "i5 eo-2x ~(o) - 0/(0) ~/2..- ::J 2. I 1 flam. Sol. gil - 2 0 -:;- () H L DE C A?-- Z A ::= 0 -=c> A,::; 0 / ~i =: 2 [ ~"- c, +Cz~1 ~I = i / ~-eX. SOCIAL ~J ~JJ - 2(J' "" IZ l-x. (3) 2 r(Q,) :/ /2. e= Pc, e. ?<. (lyre 2.) .~~ m m ~~ (3) han CL~ sd. r tk--r-' ~=x ~(f)<)='X C1. e. . w~ rn 1= 0 b~ e 212wo.- nee. &e-(2.). rr}==l b~ rx..lZ~rnu6a..~. to-Cz). z.'X Zrx. l Zx I 2 a. e. = /2. e; =p ~ '= b] =?1:3fi'= (;-z- e. ,j * ~J) _ z~/ ~ -'6 e-2~ (It) y(IX. ) -" Po e-2')(=p (4 )}W.b CL ~ • ScJ. of tL-. ~. 17) -2f)(. L. I - -2'Z, J J .L_( ) ~.=. X Q e WYl.I2f2e. m:= 0 t;eC, e. V0 1"'lfJU a So ,U7 2. --2..0(., '-20L / -2'k­ ~ :: CL ~ '==P j~:r::: - 2Q e -==P j .::; '-t (k e -2~- 2tX.-0~ (4-):::=i? '-f a.. e -+- I..t a.. e:= - 8 e '-===1/ If(L -= - ~ c:t>cL ~ - I [~p~= -e-~J Pn~5::,1. [~ ::; C, + Ce.- ~"'-+ 6~ e'2"'=-. e 29<] 1 i::llo)=-2-=D C/-tCz-/O _------- ----­ SOCIAL f<. L C - c..if(.uir-$ Po ~ at RoJv",." I CLIn 'vnk~<'JL at L J.I~/ cYMJ1 ~ UJ.F~CL ~ c r-uuL ~~ M nzrWu-, iLr aIY1 ~e F (f:-.mI )( E vef.:b.;, TFiJL. v~ duJp ~: V.t!o- ~ R~ [£;RZ, Rr] 2) tA"... ~61.. L c:n[£L ~ L-r'J WhuuLT'.; dI, L dt; 3) ~ C4pQ citam&- C ~ Fe := . w~Q.LA I :::. Q' c Kivc.hhoFfs LaW 'II We.. 0J>">WYY1-"-. ~ £. ~CL v~dMr~ - E I ~ & SUI)')') at o2J2 IJ~ ~s aJ""l8{Jtnd ~ ~.~~O (RLC-~b) R =4 -Ill L= II-l/ C~o.?-es~· E::.. 2-c; ~ t v~. Q(0) = 0./ L (o):=. 0 .tlL-- ~ I. ER. + EL + Ec.. --r (- E) ;;:, 0 . R.I + LX) + R:=;,E -==D I.;T·+X J+IIQ ~ zs~6 . c D~: 4 1:'1 + Tilt- 4Q/:::: 25~t LJ T I -+ T'l + 4I =2 S" CJ):) (;- . (2. ,.....----u SOCIAL 1/ I Q+LI(;(flfQ==O (2.) ~LD£C '2 .2 ~ + liA + 4 =0 -==/) ().+2) =0= >-. Z A Z-2. z Q ( J) -zt h-= C;+ CZC e PcvJ. s:, I. Unrlef. ut r(b)z2f)~t:= eoC[Pa~t+Q6~tJ fnr.e. 3 (J) har., tl fo.>c.t •sol. 0/-tJv- te='. -or := taCt)=- t"'(CI-{.ff)C +- b~t) whme.. I'Y)" 0 bee.. un t CUYl SVn t = nwt ~(~ Q:: Q cd + boUnt ~ b(= -a.. ~ t -f-b ar::>c ==0 0:' := - C5JJt - b~t . 0­ ~ ~(I);- (-ctCbJt - b~t) + 1.((-a ~t +bqpt)·t-4-(a.C<bt +b~ &):::; 25~t. axf· et CD::> t : -OL-4b +40. = 0 =P x>'-+l.{b-=-o=o L -f es-t et ~ t : - b - 'fa:.. +i, b.= 2.. S- -==t> -l; a. -l 3b:= 25 -I.{tl _5"'-::0 25 =0 - 2c:JCL = 25" c=p/o..= -4 ] ~ ~ Ib=3J C2.p= -4C8Jt +3~~ . Gen. sol~ Q -= (C1+clt) e-2b_ 4 OPt + 3~t . QeD) '=:. 0 ==0 C 1 -4- == 0 ==C> C, =. '-f __ J -71­ SOCIAL IQ.= (1-/+ ql:; )e-z6 _ Lt Cib t + 3 ~-b 1 "* 1=::::- Q':; fJ e- z,b_ 2- (~ ·t 5 b)tiZ6+ I.; ~ t -+ 3e»::>c [I::: (-3 -lot )e-z.t+lini,-, b + 3croi ) b) ShiYw t9uJ; T to &- /X¥m at 2 r~ IT elm<:! IS wk ~ IT.::o 6-WD r,- ~ =-eM ~ T~ ~ . IS '</:) ~j ~ S~-S~~ . n. (') I b)' o-z·f;_ ()'-3 -lob co -HI< ~ -/0 *b'YYl -0-0 v -~ --- -0 - - ib- b-)tOJ eZ/; co Z e . *- ~ 1I ~ b d~Jyd·t ekui- =:DJ&m odt1& io b-)-faJ ~ ~ 3 c.fYi -=f;- 0 ' :) IT ::: (-3 -lot )eZJ a=JIIs ~ II rxdib + 3 cmtJ c) U~ Hoi~ IdtL r+ et I cmvd Is -zt ~ [6_J ~ (-3 - iO-t) 1<' E -+l[ sUn [&]+ 3CC1; [6]; IS [t- J:= Lj SlY! [b] .+ 3 Cs> f·b]; PfLot ["F·[bJ; TS[t]j / [t> O/IO]J.9 5 4 3 Z. I 2 SOCIAL f'ru:h 2.3 (I - 1'6') 1-1 IX/( 1;'5; II/let) ~ LC -C1'vwit- L.-'" D,CS H; C:::; '6 x 104p-r=J £ -==- b20 vol-r~ I Z (0) ~ Q (0) =- 0 ­ £:L + Ec - £:::; 0 ==t> L.X j + % .OJ E­ 104 b2. ()~ S" Q I) + - Q :=; 2 t:t + IO~CDO Q :::: 2 /:;2. =:===t> Q II + ZS-CO Q. :=; '2 /:,20(1) 4 n Jl II I 2. \ ¥ nOh1. 50. \0(. + ZS"OOQ..:;;;oO==D >.. +z,~oo::::; 0 :::t> 1\ ,_ ±so;" i'-z.- Qh~ C,G6JSot +c.Z~506 p~. r (i) == 2- /:;2~ P1. .~e.... I ()) ~ a- fa.rtb· Sol. ~ ~ ~ . n h1 h1 '2. . to< -= b ~ -== /; ( CL -b + hb -+ c ) \)(/~ m ~ 0 be.c.. t 2/ b am-d I 017.sL. rn&t .dJf. I:E- (?) 0 1 Q= C0-t2-+b-6 +c- ==D = 2 ~ b+-6 -l) Q.II- z~ l'): 2 a.. + ZSm (cttZ-rbt +C).::; 26<- . /'J dJ t/-,' Z 500 Cl d::> CA.:: { :::. 2 \..AJ6 () I Z so c18f {;-: '2. '000 b "" 0 =D h:::> 0 . -/-. 0- I cervJl; : 20. +Z50d C ==-0 =pc... -=:; - ~ -:: - '-"'\'L (z-t;;o (l '2--50 SOCIAL Q =C j W::J~oh -t Cz ~ 5J6 -r.-L (b'--_ i- ) ~?$O 12--50 ¥- Q(oho ::=D C{ - . ( :::0 =:DC z I (2S07.- 1;tSb'L.­ + XC0) :::; Q'CO) "" 0 ==0 C =7 z @ RL C- Ct'fCO/'t .. R=8Jl, L;::. D.S}--II C::. 0.1 r:- 1 E -=- loo~2t vo\t-S EF< + EL+ Ec - E .::. 0 Q ) · L f<I +L-T)+ _:=;; E =-D D.5I +S?T+'OQ=-ICO~Zu c Q I) +'6t;;zl + 2-- 0 Q::= 2. 00~ 2 i::- (I) "* Hom. Sol: 'I I Q + 16 Q + 20Q 0=- 0 (2) \'2 +-I' A + 20 ::: 0 ] \. -zs + (i;i( AI =-2+zJii' I .z:::D f'\ - ~ 6 ~ 6~ - 20:::; I; L( ~ t Az =-8-z£' n A,t 1\ t \o(h =- Cl e+CZ e ~ if PonJ;. Sol.! Uti Jet', c...:xI. dt)::; 200~2l: = eOC( fc,C1hzc +Qo~2.t) (I) ~ et fani . .sol t/ ~ ~ Q-== fm(a CB'J2b+b~'2tJ W~ m~o bee, w:>2t amd ~zt ~f"YUJ6 ~.&r (2) Q =ct Cfuzb +b~z& ={) QI:= - Zo.. ~z6 +zbCft> zt . t{1 =:; - t.; 0.. Cfb2J:: -1.1 b~ zl; ­ SOCIAL ' ~.at co:> zt i - Lt Ct +3 Z,h -I- w ~ =-- 0 :=::[) a. z:- - 2 b eaf· t( ~ zb: -I.Jb-32a .J.Zvb""'200 =/) Ibb+6ltb=2co .---J"'.. .k. Zco _ s... --t/ 20 - 2.­ ct..::-s Q p =- C)ClnZt +1 ~2t r-. - C!j >., t >-"zO L C"'. 6 ~=.....:.-..--'--b~. Q:::: C j e- + C e, - 5 L.ir:> Z v + 1; ~~ z AsstvwvL Q(0) = 0 -=:::[) C, +cz, - S- =: 0 (3) n I \ /Vb. Az); .. L .L X.::;. ~ :=or /', (../ e. + AZ C-z.. e +,tJ /).ifYJ Z, C -f 5 CiJJ2c . T(o) ==- 0 -=0 A, C j +).z c.2.::1- 5":= 0 (it) (3)/(LJ) ==D c.,:=: ?/ L.z ~ ? - _ ) (-g+zJli7)t . (-'8-2Ji/')6 T - ( g+zJi(' C/ f f (-'8-zJil')Cz e +IO~2.t+~Ub2.t .&~O tJ. J b-/kD A:lIm ; 0 b-:>tw SOCIAL -- ---_._~ @ Z 10 VecUafJ.en et p~, Heftad fa-r ~f' ~ tR..-- L. DI2 [ '81/ +- ct(~)~' ..f- hC'X,) ~ '" r(t;>(,) (1) Leb [~h; 1«( ~ I + l<z. !1z..] be. £.- ~ fa- iJu,.. HLDE ~/I + tt(rx) ~ J.of h(rx-) ~ =0 (2.) lb CI) b.,., a pcm-b. Sol. eftL- fum~-~-.:::-c..-(-~-)~-,-+-c.z-C~-)-.,,~ 1 ~ [ci~j +- C~M2-=oJ (3) ~~ (I); (c:11 ~ + c.1 ~ ~ +c!z..'tJ~ +Cz ~ ) +- 0. ('l<.) ( C t:::l/+ cz~~) +bV"') (c,:gI+C2.(j) :.= Y" ( 'X.-) ==-17 C i (,~I"+ ct~; +- b'3l) + c.2 (~~ + 0-.\1~ +- 6\12..) -+ c.; ~: +c.'2.g~= 'f(oc) Ll~() ~ 0 L (~z-) = 0 =i/ ret~: + c..~ ~~ ::: Y'Cc0? (4-) ~, c\ / -f- ~2- Cz.. I == 0 J / 1 / 8{ c( t- ~z Cz -= V ('X-) SOCIAL cl = Dz. lj,V' z.. D':= V(/ .=P I sol. ~p':: C, ~( + Cz. ~z.. Ge.l'l, 501. ~ =- <J .... ~ I' =(Kl ~ I -t Kz.eJ,) + (el ~/C.2-i1J h ~ =- ( c.1+ kj ) ~ I -T (c.2 +- K,J ~L.. ~ ~ Let ~h= Kl~ +Kz'i1z. k tb-~ -6&/:fk..I-/LDE.(Z.) ~ ~ 1ft .~ LD£ ~ ~'f-Cll"'-)j'l-bl",-)~o<r-(X)(I) , iD [~=CI~I +Cz~z.] VU~F,z J-:e:: cl~ + K } ~ f&':= S~ J9l-+ Kz.J V(/­ ~, ~2.1 ~; 21~ ~ (I -11-) Hw ( 1/3/ 1;/1-() ® lfJI} +-)3 =