ca) = c,l=alaf,. - mathematicsraw/courses/math427/homework/...d) f,a ^d'+t i rpa = (d'...

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Exe'rav o. 0,5 . Sohwort , ca) = C,"l=alaf,. V$fx> 4@Qr(2q,, -20(2 H l/= 0@(fr,l\) fut V) = h,tfrt'-uorit = q?Ai t:xtr - 2&J7+,tr:€ = (,x) + vf,*l'f + n:8 . So (r*l is n6 hnte4. Cbr {cx) = 'dr -fi> rfm =f,t, -t) J c+tr1 = (zk,+D - (rI,+6; = fr*) +vfcx; 17. sa. ftx) )s cowax , bu$ rffiMq C,wea. cc) .ftx) = xitrt' *)8t Vftx\= (ze,-2 r 2^) Jcxt4 = r***i*arn,tyi-- zu,w) = tX3l,X,,t;+6? qi+ltxrr/|+i* XX,-M = fr"l *fixS.vt n"t,A" eff )tp-ffi -q-ilWn,-1.+.@tr{Dffi -A4M. se. (rn ,! silW hnox. -r l--

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Page 1: ca) = C,l=alaf,. - Mathematicsraw/courses/math427/homework/...d) f,a ^d'+T i rpa = (d' ,24(r) p yrttli > iLx+vS = (a '+ ftn') vr*vr. t'i)Xnur * n" = 0 + f,r t) {zv1T u:-\ d,+rti *

Exe'rav o.

0,5 . Sohwort ,

ca) = C,"l=alaf,.V$fx> 4@Qr(2q,, -20(2

H l/= 0@(fr,l\)

fut V) = h,tfrt'-uorit= q?Ai t:xtr - 2&J7+,tr:€= (,x) + vf,*l'f + n:8 .

So (r*l is n6 hnte4.

Cbr {cx) = 'dr -fi>

rfm =f,t, -t)

J c+tr1 = (zk,+D - (rI,+6;=

fr*) +vfcx; 17.sa. ftx) )s cowax , bu$ rffiMq C,wea.

cc) .ftx) = xitrt' *)8t

Vftx\= (ze,-2 r 2^)

Jcxt4 = r***i*arn,tyi-- zu,w)= tX3l,X,,t;+6? qi+ltxrr/|+i* XX,-M

= fr"l *fixS.vt n"t,A"

eff )tp-ffi -q-ilWn,-1.+.@tr{Dffi -A4M.

se. (rn ,! silW hnox.

- r l - -

Page 2: ca) = C,l=alaf,. - Mathematicsraw/courses/math427/homework/...d) f,a ^d'+T i rpa = (d' ,24(r) p yrttli > iLx+vS = (a '+ ftn') vr*vr. t'i)Xnur * n" = 0 + f,r t) {zv1T u:-\ d,+rti *

d) f,a ^d'+T i

rpa = (d' ,24(r)p yrttli >

iLx+vS = (a '+ ftn')vr*vr.

t'i)Xnur * n"= 0 + f,r t) {zv1T u:-

\ d,+rti * i.;.'.1/r n )1,r/z + e*'(ov'- *.Vt) +Gt-

Cana&+ f-rrce* , # q7, d'*t *tn v,e &

fra) =o.

f'*, = s*-t ,,d.* vi >t 6ttu,l >o

vr o { ,U1.sso {cw zo.

so fcr*r; - f") n vfx) .v + d k) -1-v1)+€

e {Cx)+ #cxl /

, 1;'E;-; "FSe ft8)

h sv+"t'lg 6n4ex'

Qut f,*l= {1r{[

qf-) =(ru,*)-frx+r; = yrrrtx,){otzttt)

= rfi$..*$fl,u+ Efit +v&

- fctl + VF\V +vir4.

So. f,x) is nat h,4ipx.

Page 3: ca) = C,l=alaf,. - Mathematicsraw/courses/math427/homework/...d) f,a ^d'+T i rpa = (d' ,24(r) p yrttli > iLx+vS = (a '+ ftn') vr*vr. t'i)Xnur * n" = 0 + f,r t) {zv1T u:-\ d,+rti *

$ {,t)= q?tn,

vt'xt g*i,tS

Jtx+v1= (xftvtf + (art6)

= ryl iffitt; + ) nf* rdr nc, +G'= xi*{, o iliv,+G * n6:+d=

t "l + {cxl-V + w'?,x, tgSo (tUS i> wt hnaerX.

t fti Jtt = rxf

,zftD =(44),,o)

ftx+t4 = a, Ur,+nf=- xra+4rriv,+ lrl,�ln'1 4/x,r/it+tf,= r/+ 4Qv, + >xiyit v,'f y,'+ +r,nt$)=

f*, + vfxs'v + >f,v,'+ t/,"(v,*>n)u= fx t +vfut v

f l � i - -

E e P i s b * e J x , b d M r y h r w xr'nt {,")--

Anll";fttr)

rpt9 = (hstmt+il)r asta,+ug)

-{rfX+U) -- Sin[ xtdt a>+r]t)f *

= Snfrf,+L) +ghft'+tu, +il>+U/ *aWn+A)

= ,5ingp,a4"7 n zaufto,+\b) +ry/ s;n n{'

::#p,:;#:;::'r7,#;w+ >intrf,+*,)

[* tw*,t S *1 I hskxr+lr)( t/r+t/.)

s {,"1 * \2frx)v + 6\r6y,1v,4+ry-) - eart,*4) - ,.acm+*-;c,t,+y'-)3 ------_ & #ry te nnt (bnrex ,

Page 4: ca) = C,l=alaf,. - Mathematicsraw/courses/math427/homework/...d) f,a ^d'+T i rpa = (d' ,24(r) p yrttli > iLx+vS = (a '+ ftn') vr*vr. t'i)Xnur * n" = 0 + f,r t) {zv1T u:-\ d,+rti *

r.t) {tx)= xi:atx.+fr;

qfx) = (>tx,-)frt ,il>-2kr)

{r"oul = fa,+rriJr [+,+trtyn +b) +tryr+wfE Xi+>l<,vi*,1'-2xrx: - 2fr,8^>orrfi *>t,W *+!+>rp1;tv;-

= xi-:x' rrtai 1 [21Xr'>4,)fr + (242-)x,)G +n' ->vn +rt= (ul * rzfcr) .v + ruinf

V) W f, a"o{ {. }r- &n've'X'f^*"^t-

.i (,cxS z (cz'l * u{,txa tx->) ' ' ' v)

f,.; ) : +e) * {'B) a-t")'' *rtu' & e D

=r ,f +fl6) =,f,*flrxa + vrf +{'; (2) (x-x')-B)v B ,teq).

go d-(' b @b{t4

VAF,D. . ffip {'& f' a'z' ebf*/ hr4/zr(.

= -fx) +v{txIv.

9 fCCBl b Coruea ,\a,,fr ,bot sa+>ttV hnrc:71 .

d I .fca - Arxt+bfv-+ c-

Wtl = (a, b)

dx*) = Aln,tn| +Ad>+tD) + c

= d&tbrtr+c + a,t,+ b',r,n / r= .Jix) + vfW'V.

& fUS is h*rax , W "'a- *txfu' 6wz* '

0 . 6 . @ ,

- 4*--

Page 5: ca) = C,l=alaf,. - Mathematicsraw/courses/math427/homework/...d) f,a ^d'+T i rpa = (d' ,24(r) p yrttli > iLx+vS = (a '+ ftn') vr*vr. t'i)Xnur * n" = 0 + f,r t) {zv1T u:-\ d,+rti *

,.f, .,.r,1t;, c,r.V> I,,ul4 dd dW \fft-*

at L*ds W*tV ;f] x*"P|flr

h^ilr4ls in'+*tt # a

ilr""- fu *,& 6"f-

cbt. &htew> : W $ U W, C- t"- i,"*rt+r*ty h74,t?24.

Czt*, . v&eD.

G) + (feo$*rA-x")) + tf,6tr-vf,c*r .*-*2 W.- -e)

Uk^- X +Xo

tf, rxl - tf cad[x-8' )) >o.

{r,*> - vf"{x'X:-st >o.

= ) @ ) > o .

Cc) a*^ewz, E',' 'fix) r {or * Ca,1.(x-x"S

6Ad-'; c7o s" e.ftz> = of*rl+cvfa')e=x,Wk^. I * Xa

rfr*) >fx'l + qfx"l B-Ea)

+ c-fo ) >. cfx-l a 6vfix"2 e-e)

* 4 ]s svtrtt1 tuu/t-x.

cils 'fcxt " h,J,, ttg)'xtx:-

d*l -fttx:= h,ax'" ie rffi fury-

iI

II

IIIII

IIIIIIIIIIII

frrW hr"uollv # i

I

IIl

lI

,st ()s hatls "f'"iV f/ x'& .

Ev . ,Su*r ,f e kn//ex {""rfir* e a sV}aty aw,x rf"'^a"'- is

- g -

Page 6: ca) = C,l=alaf,. - Mathematicsraw/courses/math427/homework/...d) f,a ^d'+T i rpa = (d' ,24(r) p yrttli > iLx+vS = (a '+ ftn') vr*vr. t'i)Xnur * n" = 0 + f,r t) {zv1T u:-\ d,+rti *

ql rT . ',' ftox r u^t)x,) . t{u, + u^uf B")

e"d,'; $rX+ 6t18u)-- f*, tt vftx"S'Cx-x") +tlx-nl3kX-tx,)

JlD

e

,q f''.' t' e > f..r>,;t* ?Fr (x*"7 tx,s-,&. !'* f. =Xo, Xo: = E 16 [= t X + 7-b)Xo t6to, ,)

' , to,S > Jrf"l +vftyS. tx,-y) a )

ftle, fi=) > fcy) + vf,D .LX*y)

= frfs - ry vf rD.ty-y) gst'{cx1 >- tltv)- ci- t) qw B, ,g

qrz;,'fuo zQ-t(ty) + (rat,ftn B"_y)

#

-fcx")+ *nfia1x*x) +ttx-x.l3ttx^txl A ffx> -r-Cr- tt-fx,;

+fe> > t{x.s + *fiHcx-F,) + t lx-E t)ftx-t&) Ee(", D.

(*, = (ur* vftx")(x-x4 + lx-,r,1)(tx-*,1 ct)

{ar zco;, fuilDre.90 fu*, 16 t ?f*e zre-

+ t'r,, z F,) n oF") . (x*x,)

A ) >(>J =>

+ 6

Page 7: ca) = C,l=alaf,. - Mathematicsraw/courses/math427/homework/...d) f,a ^d'+T i rpa = (d' ,24(r) p yrttli > iLx+vS = (a '+ ftn') vr*vr. t'i)Xnur * n" = 0 + f,r t) {zv1T u:-\ d,+rti *

0,9.ry,;t

iq rb hwex,irf U=X^X"

u& tt8

f m*n/)) {wt 1dtx"1'Du

w {n,l=.{c*tttll--$' n .,rL)* {cv *ftx-*ll 1n{.|orrl "t'

{rtt = Jlxtl

>fcx"ntr) = tu+ * of*,tt'l) :t t j # *n ts,)'tl;tj''T'

, + {/-^, e")Hoy'f'= (tx,*w -ffrxUtyftxt -,t+) >0-' / 2 . I j :

J ' ' . J ' \ J

:) *,d*, B,)tr;y zsi f : t '

ont# tC , . r' ,t erB-) r,t; Y z0 .

L"n &,= fx f iu ) a t

,.tfu d^aptp* ( txottul = ,{ea . 1,.,)'il't u} #"(*ytx"+rou)u'uit'

I*n trt , 4trl . (tx") nv'fe")'u . i{,,d,y (x*Frr) tt'�F -

'' . Jtxl ̂ {s,t -ofms B-x') = } frrfi,rcerqu,y "o .

"' , ltzt,I*, "vfs"tE-e)

-*/-