+ All Categories
Home > Documents > v :] - Department of Mathematicsconrad/f08/hw4sol.pdf · rX-z-5 (x:) -b/' ~ X . 6 . rf ...

v :] - Department of Mathematicsconrad/f08/hw4sol.pdf · rX-z-5 (x:) -b/' ~ X . 6 . rf ...

Date post: 12-Mar-2018
Category:
Upload: trinhkien
View: 219 times
Download: 4 times
Share this document with a friend
10
_ f-- 1 >tJLtJT(()rJ.f ---------JJ. 1f-ff I l @ V i 5 IlJ ((oJeJ l.I'ldt.,r CJ.JXt5Ifl. --- 2 p&)/ X2.+ x+f V r,{K)- - ,X- +X EV gv r :; 2x1- I <I V v 'u a /jo '1201 L Jnk.r-.5 (tolc./" .. 1Ar!/£' ,A'07/1 bnau! , :I ',,," r(;c) EV IF' lot'< p(x) -=,,0, "- «(:J ., f;", t/ (0 V ;j " 0 j v /I.!e.r- () tiJ ,1', OJ :] S;; L '-' o , !' 0] -.I, AfV Cc,J II- r l?1 o I 0 ckf(Jtri) I o.J k kf 8if II @ V ;, ift<,1- c(os£J U¥Jkr aJJ,1!"c" J ,'f f{,j -;: 2 ,J U J:::2 fJ .. , fry 0)- ( a,J ;. f.tj f II _ 0,,, W a&u V /5 C(O.k J vfl Je '"' !(4(v.r (\lie; I hI' /.L&ir!-T,.-. ® To J"" J' (s) i 5 0 w (J.r .s; r U< fb 1jJ<- (O.vJ 1L:s-J Ii lAIl1 r J,l/hoh 6:/1J S(Ct!v (}I1J fLct arCS) ((J --(i) iJlck/ y 0" p"J;c f 31) fAGr (
Transcript

_ f-- 1 >tJLtJT(()rJ.fH'{I(J1(w~~~ ---------JJ.1f-ff Il=--~-----_. @ V i5 IlJ ((oJeJ l.I'ldt.,r CJ.JXt5Ifl. --­

2~" p&)/ X2.+ x+f € V r,{K)- - ,X- +X EV

gv r f(~)+ ~(X) :; 2x1- I <I V v 'u a /jo '1201 L ~1LJ Jnk.r-.5 (tolc./" ~'v1 .. 1Ar!/£' ,A'07/1

bnau! , :I ',,," r(;c) EV IF' lot'< 0 ·p(x) -=,,0, "- ~i «(:J ., f;", t/

(0 V ;j " 0 clD~ j v/I.!e.r- () tiJ ,1', ~

OJ~" ~~G :] S;; L'-'o , !' 0]

U{~):::c4Hf',)::-{) -.I, AfV Cc,J ~d/).J- II- rl?1o I

0~.,l ckf(Jtri) ~ I o.J k ,t~ kf 8ifII @ V ;, ift<,1- c(os£J U¥Jkr aJJ,1!"c" J i~" ,'f f{,j -;: 2

a4~ ,J UJ:::2 fJ.., fry 0)- f{l)fJft)~i.f::f: ( a,J

;. f.tj f II _ 0,,, W a&u \b~ V /5 ~IO./- C(O.k J

vflJe'"' !(4(v.r (\lie; IhI' /.L&ir!-T,.-.

® To J"" J'(s) i5 0 w(J.r .s;rU< fb1jJ<- (O.vJ

~Ll.v 1L:s-J Ii (.{f)~J lAIl1 r J,l/hoh 6:/1J S(Ct!v !ZttJ/f)i,~(,t:,

(}I1J fLct arCS) ~~kJh~ t;')(I~~J ((J --(i) ~f iJlck/ .5/~·<'o •

(~fL /kh',.l~u, ~. y 0" p"J;c f31)

fAGr (

l HOMt?''L,eJ- #--4 ( /l ___~-:-~------;-I..V_Ol'--_---.)- __l~ L~U~700~f\lJ~

T-I ~11.w (r: .. _h... L"'- !1iN. <1./,(...) ~ VN <;Aj Jcd,~ J11Jf,w-;;c~-~J/1 kb,t; 11, J c;j{J) { c 10 c1 {)'1~- acJ J,Ji)V1 tt/lvt ({- ulc.,· yhvlt· I - 1.L , l- I '( (,,/1 7

tU ;., r [ ftS JCr) I.S C( ('QO f v.1""-C' fc".~ " &c~ '.J< ;f a?J J 'IJ ",

S,-;'J I.. rN ( I1v~bc- f, eei, /, S l' S (",). (HJ[s) 4",," 14 f< ,"<- J,

Vow I!-' )" ,t 1f". eIjl J rOf/'/ h'u

(tJ g, ,1../.'.,1)•• (ftj)6J-/(;)fJ0) !if- -<,,4C\ .sc{, {I (~,l JdI

{6) ).,; J(J) ti"" r.Rd J II ...L" s. f{J}ty{f)~ J tsJ ~f6) ~, <'.,(

51 S 51'" at!d,lioA J 'eq \ ~""'~t'J ;; (Olk,,"t.f,'w. fv) 1;; <411,.).,1>,

1iJd{s) -'(rtf!)f ) _ R,Ji;" -it,D .Ii ~)I-v, ""- ("... (ff;J) 6}~ 0,f)(5)

ttl ckJ IV,

(2.) #.5 I~ f'<- I-- (fj C. Ifcc. "~ ',;-, ~ A.JJJ ;~ d 6) La"'" ,1 I. /"U ,~J<, r .J

~ k,c. A)n w ~, J re-tuv-llJ U Ija/~ 0 F 0 /b"(2,) t k t 0 (s) ~ &­{fr-o){c;)-:; f!<)t[ (r;) +(~)+O ::?-f{S)2­all "lp"fJ SfS-. [/"1

~r ull t- & ~(~)

elf) Gr'w", ~ +c oj(s) de f,'u & func-~\" j b!J

3(».::--f(s). T~~ (f7J)(J) :::f(;)fJ0)~ fid-ffr)-C W~~ (Ff3)(5)::::- 0 (s) wl, ~ SI'l/q.J ().I fft) j (> +~ (AdcJl]..\~ ,Il vq

of ~_

Is) G,',/.- AEll!, d {'J € ':f(s) ft,c.e. /.,<"'

A(ffj)({) "- HH~J j6)1 gol ~J"""I ();~ <6.( ~t { . /- i{s) fl'lJ :;cj) 4"'~ J~<J1- r..~( ()VN.~~J ;0 by ffy- du~)1u()Ve /c.,'V

ill IR ~1C<V'" ACrrJ~jLsI J ::. Af[s) -t AJi) ~ LA f)(f) t- (~)(J)()K

S6 A(ftj) ~ ~ +1 Aj

[-=--=--=-~-_-_-~~-It-&~-/ -2-~_---~~__--J

I HOft)fWoQfC -#-4 oLUT{oNjL-----------:---~-------~---=:.----~--~,

(b) h.l <J/ 1'[. pr6fof) {:;}J 1£0 (, I,ll k CMX d ~ d,dr,/' ,N(k (tL«!

J9r fe~l VJum bus [:t) TLJ k,l{,~.J ktuvj,. Ml!/~r';(r.~~'l of' r~41 (lV/'llL'l.Vj' () OMfI1LJ(fh'v~ GLU+

C1 tl~ uJJ ;~Vr1 pn,f -Iv,,- (I))

L~) GI'V€~ f E 1fsJ ~ h~v£

Ci· t (~):; 1· Hs) ~ -I (5) JD 1 f := -f Tl~/'(~I'$L r ty£ J'4W tL. . 'J' lJ) -~ Q lJ c-~ r l' «. «

® Lv ~ a. .\It j, f" c.e. c f 1R'1. To L f1, ,) ;1- "fh~J fu f le"-, ttJ W II C;(OjReY IlVlt1Lr- aJJ.,'t,).". Qv'!) SUi.(r;.V' I"tv)1Ji/;( 1--;)1 (..Ief

T~t,v1 Lf) P.5 ' "~)0;'

G.+ iT,) iF, c lJ. 11., ifr :; (XI) ~') ?( J W,) <,d 3, -6, +- 3"" 00=

U/lt! (IGO IF). ::-(X~(~L/..(2(()'l j al\& 9).- ,- ~'7. + 3(..)':1, ,0

LT"(tlf; :::: eXIt-x" 01 ~!J~"i:-, 't22-r lP( fW?-). T6 sLc4.> U( t-~ E-W /)J~ Ned

~ st~ L~ I +~ t-J - (~( 1 i,) -f 3(UJ, t (;fzJ = 0 ~ Tnt;ke& I

C~II-~L)~(t( ll-,J+3!v/1tll1.) ~ [~,-i?{t;,wJ+{jt.-:C2f]LU<) ~O7-0:::: 0

5'p (i( f-Lr't, e: W

AJtpJ Q~rUIl1P- lF6;W CP-tJ ).,~(f<, 1~~ (;:::(k(~/?(/.<J,) 4,d ~-?f']V =0

il...\ Ai; :: (), v)J) 1{ A"') -t ).", !-11 f ev "" """" ;{, sk •u'

A~ - ~ f3(AlV) ~ (:, T•.L<.o! A~ -.\~ <'.S(r\lJJ "',.\ {~ - c-I-swh)O ~ 0

SoAv e ~~" 5u tv (( c (o,{Q) (j/7dt./ ~Jd/)fbr, ""J -fce-Ie./'

M~[tr(~u.hG-"- S~ w l~ Q fulsf 4cR oj !R. L(

l

\1.- ---ff-()-rt1~_fC_d±_4__~4J_71_C;V--- -)

\ .CY 't .!:pt-. (). JVl,p-w. 01- /1.<{ !Je"w£ :1 I~ ~61- ,,/41t:d .d.--.

L eXJ/~Ct1 - E~i(Mfl" Vf::: {Ie 6(~ o)E tJ U1J {J2 ~ (6/brO,O~L~

g(J~ U"; +-0'2 ::::: ( (( D/J( I) fiP ~l('() ~ { l..f'6 -,.+() '2_+)1-= 2:f/ (au (J a&ll ~4ve _~ClWf\ ~J is vlc>f a JJ?(CI( ~ Qd<. /7:1 /lvf)(~

c(o.se.J vl\olJ.r (: 4 I frv1lJ Ih'r I,L4 k fJC<r- "

o UJ \J tw+ G. (j"rCj[~ ~f- rp, Cf L[tAVU (I- /) C (O-!e J l//1~'--liCIt

{(-~f(f/ wufh/);- ~f,-c)rJ. f,\raMp~' {f= (~olc{I)f-tAJ fr/)(~ I+-J-:;L~ 6

LJ - IJlI ::; [-fID" 0/ -J) f{))

@ [u ~J 1\0 CL Jv~.>ra.u of 11< I.[ &{C-YU (}- 0 'l~ / cloJ.(J (;1.k,~

~-~ttIY It·~ u(:= ( 2( 1--/2--( 2-) f- W St"r, ("c Z-z..-Z·2:=:¥ ~o

ir- ~/ -1-1 -I( -3)fW :5(11(6V1- L ( ( (- [) (~I J(-j)(-3) =- '] ~ l)

gut IF;t~ :::{I{ I( 1/ -r) clw -V'nfe- I . f .f .(-I ) ::.- -- I <. 0

GiJ l0 ~ q £U15(t£ (£ of f{2, t{ ,

F; r l w... It-\! W;.s C ((}JA..) ()/lJ.<r- b1J;) /:}'::;:>I\ . {VI/Ok v;) If; C WI

T~V\ ~ ~ (o/J,-l!Jrw/) 4 1 J 0=; =[c::. 0/ ~ lJ).) . ~tI IT, ii;:: (0, ~ ~ w,rl/z ) C"(/J

N()U ~ iv s~CJI.IJ 0 Cj c loJe) 'INkr S £-~ fc,- tl.< ~ I:J...t I; c c. fr b.1 .()JI.

'Vr("'oe ij'e-lJ ""q C /fZ. T~. (;C- (o, v, a, w) /J. --\ IF ~ (0" ~ 6, ~ w) -ttl ~V ( dl5Jed CtJJ(J~~,\ (£~) Jc~/CjI' lllrt lJ )ht !;;4, hl~, So /1-)'jUIl1-r

4. 5v1,S(u r;t rt !{fl

."

"

[_- fJA-_&!?__- __

a= HiJMw,,(L!'- =#- ( __~_()c_lt_r(_t)N_J______ (3) [0 ~ lJJ Hul'"' V ;s CL _\ JJf~c-~ (up V1W 1, c~,/c cf())o-,,< v,,~ Q)J()-,\ ...

a'll fc;q L.r ",vI;AC!~c(JJ~,,_ ~J ~J k: E V

T~~ ACK, +)(2-) ~ ttk, +Ak :::r+-b~ Z b. 2l? =b r'f ti'!d O~~ ; r r; ~o z

;0 if Ls ~ u SvbJ(J Gc.e (t r; ju. 0(\ ~ (,1L- ~~J ( rf I=c; t~1\ V '1'( Ct&o C{C;-iil) WIlr- SCc,(c­

t\tvlh~L:u k)" [;~0 yr'vt"'. )(~ v' ~J( Ae-ff- lve ~aWl A('Ax) ~ (~j~ ~LAA)~ 2 ~(Ax)~) ~ =- 6

{? (rti~ U {OJ G f,,~ !Cl~ 0f 11(' If G,d OJ ;f b ~ 0

/?-"\ W~ 10 wr/t [/] U<J (I~~v" CO'"l6rI\(J:~ of- ~ If. -u()J&- -t C{

~ f) 'lJ J

{_{/ / Lvt ~ fa fp~ Uv~!L/' f/v.( ct-"'e... ,xl J c\z. J d;> J", /J, ~ t

~([l] J cI, C-t]f~3 [!] ~ (/] f'llJcJ~) [M~f\~)J JI"'.I> VJ fh.. 5yfh".!'1 f/f (!.l I/~~'l./

LJ d I T 20<, - 2d 3 =:- (

2 rX ( t- 0<1- - ex.1 ..:. (

-3d ~2c11- ~r (

{

I:

fi.epr~JVl hj f liJ .5'lf.t IV' C<o Ct "1 Ct u- tf,J,1'I~) (l1t.J'r (k ~ J. MI.R.

,1~l.- I ILf 2 (2. \. 1. 'Oul ,Jet... {,'" fl.,-j I.{""-'J [:'

2-

( L

o ( o

Q"-- PA_&f ~ '=D

-----

f-{tC'lfW>((!t :IH{ 56 LU7{w' Jr (f;) ~ ;i IA,;T q If,..<" Cv,.k,'M TI" .? -f ••J ~,7: w-rJ-e h v J~<~

u. {,'r¥lW' U.J(}I.~,'",a·ib/i I ().h ~ ~ov.lJ fIfLe.I. ~ (>u.(e;.-.J) 0<, t... .. ) 0('). J"

(Lt< t- MLxJ ~ 0< ( ~ {)() t- rX-z-5(x:) -b/' ~ X 6 rf­('~i k't::=-o<'{~;n2.-{X)-t()l2 (fOL.{x) 4r.:!i Xff!-

SWt l1b t.tL (pr all Jc.f(R / (f k6{J.f ~f k.:;O - N()jJ/~ K--C:; ,'II!" DUr-

O-ylJli.!J\ j/illJ O'J.;:;. (-O+d")." =;> O=CX2­

Sv ~ r{k~5' If\j i" X ::: V \j' Ve.J 17" .. - c>((. D1 O'? . I ~ 7r L D(2­Uj

~ &., J. ()l.2-~ 0 0" O~ k.,.J ( 6 (. 0-.- ~ TT L 0'1 -Ii IJ rk,/\ LHJ TL t ) i.J

~ C6£;If-rO et,'c. A'o /f .J J,p ~ c~" (.u;, ~ be. lJJt'-~ rr t; I,het(/' Lb."l h'V/Q-A)", ., I- .( c.,J t;

cY k {~ (, li~aI' (qM~'",I"", .f t a,J j ik e. V"" v

r t;, :: (S·~ /() 2- X f (.5c C7J 'L )(

[t~r CO"1!);(li(,~L" vi- {("J J to.r C~J I'M 'I I\.I~J

CoS (L Y) :: (6) 2 k- S ;'1-, '2-Y

(4) ~ I) wi Ct I{~av (.c~~/·~lI~.'h~ o.t- -f 4/7,) j. f £{'1J :1 Ci.J1~ftU.t.dCl"""

(J.,).. \~<lav" OMI';I\c.(~OIlJ 1- (p,.,f';'I\VOi.-J fv"~b,,c- u!tt co~Ahllcu..J. ~L-f h (£ 110+ (c.7() ~f1. \}..OV-.J [ e.y - 11 ls dti(0 kr/la14J r; I k ~ --!F ) 0 1:+ C"" I J­

PD.(!;,/b~ 6.0- q (/NU,v- CUM0"'14'h)1l or-/- ",d ,5 .

@ Am I:~(,. of SV" k '" s.e1- /5 S'" i 'I X, x ~ >< 31 ';0 " u, oJ

poI7(1vr'\ ~ \ (Q\ P~ IJ of- 1J.. ~('A ao .. / 't c{, K t- Q'1- {' 'L.., Q ~ '33

(~~, Ttl; (' -'lo>'- ~ o)J pOJJJ1 ~ C('fw.<.r-,).

{.X(jCD No SUG ~ ce. ~ P3 '5 4 d;fh<."'J/~!I4 f It~.JJ- nuY' 0€. ~/'.5 ~ 5fCiU\ P"3

l

~ --_H_~_Mf_UJI)_fL:....-r-_#_Lf_'_S_P_l_Uli_(_OI'U:_S --_--/-1 @II riX)r? td EO Lu 1/"", pu<J:=. 4, k 3r bl ~ 11({, H-b, Q,J

't (x) :::::- d, X't b./t-a.>.: r~? - J. pOrt (~):= (IV aLJ 'i If {b,l /,Jk'+(q,l6,){il£lbJ Lu&~i~ ~.' LA lu- Sf:, W r~ C{okd lAttd-ftl' t{;J,d.;J.,t., - A6~ 7/V<t" ~cre c.ve

Ivw" C~ptl;'l ). p(x) ~(A~, )/tiJ)J~ L+ {AqJ HOb,) I "'h:cb (~ W;0­

J;, W II c[olQ) Ul\~/' fcdc.v f'\tv/f)t Ic.~ht;", o)v 4J 0 fA 10[,;!'t( .e.

/vow le~ S =£x3tX~ x'1---t {J < [U~~ ~k~J ~~ W (~ cpf ~ £,ftt

a.><J+ht\'L-fc{Ktb~ q{K'Jtk)+bC-tL-fI) J,"iJ l+~ a (('fIIltj."" (6/{0/J1c~~-1 ,,+ e ~'\U,"\b vI- 5.

© No. ~"I.I ~ J;n."I}.041 Ji.c Wo. ",~J of I.( ue,lcrJ A -;6"teo;(- ,-:J-,

oN_ Tf a1f'''l -f. w" '" a.·bl'l.roy e{."",I- 0>/ IR. 'i ~ • /1 ~ iV-­. f,k. ,0" ti..J

L h f it (j~ )'f){.J 11'\ S IJ-li oj fz..,\ -f/v;. .51{Jh./~ , r -e (}l/.r hl..t....,; r... c;17l1(), !\t.r 1\V/l tJ 1/ I

(.'1- 3 5 0 C( ~ 0 z , ~ b

o -( -1 -2 ~ -L ~ 2 Z -( 0\

en .wl'tl'e (./ 4 .. C(i'~;trltti) i&~J ol J1 • ()~

3 ~

b-(h/j hec,,1t0 l­-2- -~0 l 0

(>D 0 I I' () 6 0 0 0

~ y.. ~ r.v'f) e~~( ~r~ , 6 4

. 1b;'q--q I I b I \ ~ 0 +1 -:Z-c

-~[{ .. J..btc­• 'Z.

[----r-(lGf----=:i---~----(

eWL_------B-f-ofl1--cK-k_J}-_{~(_)"__L-=.:-i1~7(-=--d~_J__--__ L '<J ''I([) ~ 0 j h/-tf\JJ ( tt~ 1',<. C4-J r- \ pCV'I 8

4,.J;., pCtJt f ® ~ 1-(;/11 0th..,~ '~~l/-l(@~ S_ -I- t·~ f/'c ~y

_, ~ I '<I'- 1/1'+ ,J (~j1';; 4,L ~ q/; riJ>_f)J L v/t!()A;J (7;L \ ~,C (; ,A r./

I o I 2..

c (;; C

o (:, C.

,j)k- /f~ >{:- ­j ; -27

1~ t vJ; IN

<:,) 6

0

t.J ()

2 -( h, D b2.- 2...h,2

0 t> 2>b( -3~ fb]

-<-fb, f2.L t b'(o 0 C- O

~'fJ +(1) S~J 4.~ (~ lI)k,J I'? W) 0/\ ~ If­(0

---~~ __J

L_ cgbl-3b~r-b3 =- 0

~~~ f2J)Z- f-~'(-O (

5" fu.l~'} fill 5 )1~ 'V ,\ ftv! ~) / LM Le L /7, )­

tfl} rU3 3p'u tl s) at - hr <.~~(

~ NJl)fIiA""'I!iJi,. n lIe)"u a-.. I,~",& titfw'!"',I,

Lao ~AI~ L [U t [i] ,[i J~ ['I]

J

r _------H-·/){L_Lf_C_ulI_'f~__1t-_~_J-(.-~-(j_7{_d_JJJ ---~ ~ @ ~, 5Jff'f;t ~1'J,.j~ _Wo _

d I {li, .,-~ f-(jf ~L ( V; +u- ) j-.J] 0', =-- 0

I'I{\ d,V', t(d/ frY;,.)U'~ +(..,(, i.xz t!1)~ ==0

B) J; /~( J; II'tvurl,y L~..tl~J / J u I:)~(Jf\f.

0( ( ~ 0

J l rd''l- :::. 0

-b j -rr/.. t.73--­0\ I '}.. L

1LJ >iJl~1YJ vi- ~p~h'l).I (i/)17 ~v rf1te

{ U~I l' ()'l T u_? , !F2 1 ~ I U 3 ( /;~~(;.-!Y

r~). . l{'~~ "& _~. T( u [kn , I~II > <-/IJ-rl !l- u. J Cvr: Il~llt/'~ rkt~ck-, J­

(fj;Jo , T~ >I<&~' ;~ S (1< rr 4 t{&f- Sf"

(0 rJ Ii, II... v, J':J )~ s {( 1'<.< (J J (, /IA'-'.<A.!:J ,',1 j~f! eM~ J-.

® L s..) { i ~ ~ t' t t 2.,.."f+I j t rt"+-{3 ') f,M..A~ loc0"e"),,,,)./ /,

tw «, ~ JJ O~) Va)", {e, f' ~"''''' ;,I j (1" + ,'0 r!,.,', (f c", ,f Jf,7( k 11'w."A~ "', pv>h/ll. T~ 'I" u it .w J rU:J~~' & ufo ft,. .(,/,.,

~ (tYt-{>tt \-tfl) 'f b{flf-f-'--rt) ~ qt4-t {ftfl)t-Jf- {G.f-b)t 2 ~ (ttf0}f-f q.

JJw; 4 ,'> /2) ;1\ ~ 5f4 111 I j ~ { t ~ f{ 1-rt').t IT 1/ t 3rt 'Z--tt-/ f L.f] ;J

~ L'1c.1u~l) If, )y~~ ).(,;- .u / TL- ~ t 3 ;j It 0';- /" ~\fi. 5/CiiJ t: l­

rkok- u~ (~U9-- ('f V<l,./'f) 111/) h} f;' J ~ fJ.e Sf~ C<J ub'~} -(6

i +\f ff\ trt /.Jt t \ t/ t 4/3} i) I; "'b ,'0)9"- )",-,/., i2. Ll 1c t ;'1

4.~" of ft.... i( §t'-tf3-rt'1't-l-1/i\-t-l-t:/ t~lt~t:~ i.s,"1.0/

C'rv ~" G (n ~f1{~.).v,~ t·l cJ.s t ?u.r---i P J, 'J- () hCt I J) +- 1)i,.t) (.I"'" ry

[ rfG-£ {D ~-----------------------


Recommended