,ffi,g)u(A'ng') = [t^nB)un, J I tbnB), dJ ,. pistnbuhvetow=[nua')n(6ut',[n

[aue) n (e uo')J 6oisrributive kw=tEn(eue) lnthug')n E, 1 , .a r ,orversqlqwB (eua1 n(nu$r) rdea{tsL, , , r= (AUU) n (nlUe; sa co'norutat ivQLqr^r

Find the eqqqton et {rne cicct{ wi{h cenfce (zr-3) wh,ch ho.rches *{te slrai3laf rine4x-3g+23'=6. (+1

Rqlius o{ crrcle, r slror{qgt iis+orsg {rotr A to {te liac.----

Elue{io^ o+ aica(g r= !., uait '/

( t - r ) t+(J-(-31)1=gz 4l r-hr(+lt + gl+bx +Q = 6lt

, (a+Ja-hl l .6x-5t = O v/^

tQ, cea\ vafug of x and g. 161

$+ rlr o ,/^

. '. ltgOr g:O t ,(all g. O t

so= +. = I .....(D t'c i9g ++ = t ii ,:;= f- | =i,/scr 16*. . . . I AJt$gJ=+ lp ' .OL=E

l - f . . Tsord=*.=E6.^ 'E+ q=o

t 3 +r/,

@*"€unc{ion f is tl t Y1Q rind{hel,,,.r {cr,; ar.4 ri,'l {cr;.l-a)* | t x>rg t-eg+ rr0-

r'lence, deterrnine whrAlIg: l irn . {(rl,

t(to?

nt i 'vr-$tr1 l0 r /

@;g*{trt+.g-$rr, l+gtil|b{trl it not .le{iaedffq,nre, ftr; ;3 aot (ontiouous qt \=0,/

' /anlln, .

y ' a lx2ota

gand /5, as a secies o[ q.scendinq powers o[ x q? h and includinq *he teca in 13.s.rbsfitutin{^r = *o, €ind aa cglroxirnZfibn foc /jq cciccect to 4 sig'nificart figuces.

t+lr4 l

Antq(: I-(r+1xF + rr(rx) * td!!:!r(z*)t+ trg{$ig(1f,f+,,.,. ,/T3t

el+r-* , (1 +**?*. . . . v/(r-r{-t= I - !t-r,,1+ :t,(-jl.-U(-lr)z+ -i!t!!

= t* rt + lrrr + !*r11..... ,./ tato

f f i r l .o4o83z ,/, lg * t 'ot+O87L

6JA * (x r.o+0832 ,/

6 d 6.2+5 (+r.f, .r '

@,*: ?^TiY{,i,: s,:.1i1^s,^.fl::tY3 tl ?:'rl^ !y r:t!1-1) o{ r= z!t-l) . fi .p i1 a. poinl oo *\Ezuc\re 'qnd O is {\ie o..Tn, shgur {+tat +de4ucve 'qnd o ts $ie o..Tn, shgut {ttat +he efiotioo of *he locis of A which dividds o? i^te;;cll,i

l*.J,1To;',1,11 5i,ilil"o:1.#liJl[ f,1 -rr ih. no.^"r oi iJoii.sil,;yithe point A( l r8) , *Le ioordinqles P. t6t

? (ttt-r;r r(t'r))

?rt =l+z

)G= &,)

3a =(?u ",X 3y-')?x=Qy).-( , / t

ja

d,rfis6cadi

3r+ ),./$ = tt-l

95= 2jgf=-Z

- f aJJry* --tt-L 2(t-!) - t'?at o{ aorrrrnf t frz= - (t.

33g =t- l

@x = [}u+,X 1-g+ r-z) ,/

3

J-t- lt -rJ

Frorn

@ 4rHdieat AP = 6radicat o{ ao(64[ at P hgil xtalroosEl

- tg3, t r t -3tetR, ; tg3 t / coordiaa+es P[aCr -L) ,2( 3-,t] = p(A ,I) r

r}-(k+z) x-+(f+s; =O, artdbo-tln x ad P ace gosifiie 16leA7, E+j '

H-. _. - o, . r , ^ gothdrP ac€ ?od,t iutr t(p>O

Xa-(k+z)x+( la+S)=OA-. . . i , ' J . kt i>d

. , ' d+g>or- I k+b>o

e k- ' i t i

Yt*:o(&p ere ceet rrs*S then I

[-(r+]) 12 - 4(rxk+s) ).Q v/ I t* - B<]f -a. . . r - - t^ - t ) - t^ ' - - - ; I\ rT 1t- - . t ' \ l / \F?u ?v v

Ikl++ktt+-+k-to>.O I t (C-?l(g-?l>O,, ,

<+ . B<-t

-6K +rl.O >O

O.. A-t

Reocr

--

i l

oz

ro.{i

,/ ,/?(tg+? s Z2r+2gt? c 3

r \ i , r fb T f t t - c '

lu.Iln lhe_gra$ 9. lr3 unl$= {?r +30,

g= *r

ra,+ - ra4l

f tr)= tt+ 1x.- 39

, ?.1 ,/

3o rrtre, coot = 2.813 (3d.1) €

Le,t to = 3)l'r = 3- Lg). ,/

:2.Eqf;!?) ,t(2 " 1.t15s5 - !,I?g!E!). ,'

= 7't130s '/i' (l'8l6s5J

tt"r.gqios- t!..8q39t= r.!{No{ EE'?l3os)

fcr a 1.8t3otr - 9(r.8q393'r

3l'tqlo* ,9@)

i)A-rf?! I \11\= A-t( ir ' | \$ l l \ i l \ ]

,

It

f,

hqs

" Jo.'"--u- , -1 ,nt^lnon FVrocrcd {6 3 slnifiCortt $gtr-r-eS. Lsl

n"A {,tt exart Ua.tue oF V. L s 1$s.. e;e+i t

er i : :* : ' l w-s-B7s'It*lti"d-o

l;: lxli li:m;$'il:li-:*s,*,s*)+{Vo\une,, V' Jt:'fl5/[ ll4 ll^ l.:la l '8

)=

{rtr} a 3e3+ 2!:R Lntr = )Ln -

rhe fwo 3re

e@E

l.6tlnl.8)*utl"l ,/nr

= l . l l ( t r . l , ) , /EXcgt VetuQ ! I,r{qa.foa f c,rh J u.#*.,trc =(uXv) - J,v l.r$) a*

. , 6* \ / \ t J 6rL '

=T[o'-. o) r' [u - r^(9.*u]i=1[i1t [-i+latu+r)Ji I ,/ U.8

Tht al5,r^f h+.r rrt x: | , J',Cu t$-. t .2. f - ,1 l . - . . r f r t ,

9tr !+ l r

f-p , (rr-rtl[-rJ -(r,-x]LXi.l.rl ffl, , (2G-t \ 'L- l I - (),-x l L)(r-.r. rl (3r: -") ilI tY

- l l l l - rZ l Aiarrhr l f l((tt-f)t )t

a al^l..n

t f , - t) t f f i / wy'\ t r I i \ * / . . Dlroa*l \ i - -d,-,Y ,, Dirrqc.tl r r . . - ! ioaA*2

=(l- t ) ( - - ' ' ' ' r r "

u=htggl N,1fu=t 1. i5. ,S= F' l"'J'

= .ffi, ,/ rhil;#.il,;;"fi'v

O zs x t i * ; t ia lah no'nyo:tz bukaa si far

MoRA 2* = r ' ixt i r Z- Z ' . (ct i r ) - (e- i t )

= ?i t '

l ltl$ F

= ;<-fr

ST PM ,qqr Kr

; ( ; )

3 i(r-ir)aI=r?

: !zr f l r= r (z/

, lMaha V

:

= r-x-xr +-g-ry"la,' saL j;ka tg. | < I rL'iv

nno&a set lUla,.'x q.njrrls

fcn6e nba *ya.n ini sah 'ralafi [tf - i ,* <tl

Qa,n*ilcen x . tI( , -i)' = | -b - (i)'_ f (*), -E G)-_ 3G)'

t f l t y a.ssg 1186

+ ? o.8ss o8G

Si = r .?rot7

O Pets.tto-, 'r +

funcar o, ,

Ph'rakc d+

? =

dP=

mt f 1=@ ,l\cru?tAlt|avr

-1y ' -@

^ -ctnxt+(zn-, ' | . )x+n=o

o(. tpr

- ( r i - - ' )n

Katqleart ?ofo" *

rEairF$Fya' l PB^ca

y

r .aFa o(,+pr s

d.*p,=*- ' -C9o{ ' P, = *-- |d,F,: | - -@

d,oeo, *=(1lP) 'dP

.r, *p, . (gE)'- .Sadj

d, *p. = +T*.@tCA, d,* f ,=

(a,) '- (#) o{, t I sJ

o(P (,(, )' - (ot'+p') ot, t otp : o

(ora,-P)(pd,-a) =o

d,=# * la ' f ,=?

ft,h'la {,.t ) f, = &) =+A7"l l t^ , ,= i ; p, =6 =i

A:k b^aoL: ,.^li-r" + , *

hc,, lo.*: f . yt ap (*)

Ac'- ' ' loP'! 3r ' 'Ac'= ?p'

OteJt Fcralra TC.3l tT, ,naf.a Ac. *AT(+*11' ' 7p

4' ' 72)f r | .+ i?so.66tp

Lg" 1c " 3if . ff.n a t.ltg p

iod. Af .o.6etf , fc= l '?7t tp.

@ c r- 3..) i =

I3+ r .7( o

Kailk+r, 4 AT8'0 ,DoJo'-- aegT , fT

sia36

D*lan aBTc, #o' fc

3i'|3d

@io ;Tc . shT

Dalu- A A BC .. ACa.

r tf (-e.) +(^ttt,t) ( -3-)'+ CI(i?(-{'' Gt*s,

+ (i,(-;X-;X-$) (-rt1e.T

+ (tX-3(-tf- BX-*)( _g.)'+

=# _@

fta't ec'- >7*e7(sc) tos 6o'

Te

@ r : t ( t l t ) -4

U=:(t t t ) - -eDa'; @

6e^*rto' t' !' t fu' dl^ @

* = ( { - , ) [ ( l - , )+ ' l

'= ( l - ' ) ( {+ ' )i i :

{ - t

gx = y ' -g

9r = V' 'V

J'= Q(x+r)

\iD ote.L Vcra'ta #oJ'^ 4*n q.^ji Idt.^ Ur ,",. lta (e1l'*^3 o J

barrimr,*..' ge . g.Isi - x

Ctch h.ca.te V' 2 o, n^ofe

h(r+r) r .o ) * 7 - l

?f . galr l -1, J=o + Ks- l

?r. f .eo;-y,x=o + J '=+tJ ' ! ,

L.l.a.o.,n 1."0*T t'. +(*+r) aaalo.l"

*(r t t )

\ " .b: t" F4to,J*1oo

| (x1 + !(r) = r" (.i#) * l" ( ff,)= l^(.i+)(fr,t= r"Ii_+:t,i:;J= f,, IJ-.(ffill

[ . , * ( f t lJt J( f f i1

f"" i l , grr) t tQ).3 (rur,

( t )

C9 J(*) s

3 ( l l =

l "

(n

O Jo Jl i i 'x =(si^r) t

# = | csn";'t crn'*1 =.,ft-Jr-

cr'

:i

t t

i l- t

! {-9L

(sin r1+(-st^ e) - Fr r . 1 f,P*rrril

= -1 - t ' t ' -$ i '(s ia x; i

= -) _+ (r - -e.J- l

*J '#=-rr*-( , - ! r )

. . tq l D *, .1 - t , 'o,) 4r' J

A J:^t* , dxQo..lilcarr t^'= l+X I ! r^du = Ax

Ape,bi la F= o, u- ' I I qt I

Aicbi l r x. 3, r^" t l * ta. z

Jl .fifi dv -- J, c *'- r ) *( zu J-u)

= 2l : (u*-w') tu

='[+ -1]:' , I (+-31-t*-{ l }= 2 (2i - i l= z(#l. .+= 7+

=4,

- -o l=l

) + . . . - r [a+t ; -44J +_@

- . ) dJ-, t 4 j(a-r) a l l

t )dzsctu*a'r k 'z 'n

ik" f (n i laJr , l+ . . . .+ at lr r I+.- . .+11)

) Crtrr)rq)l5o

I t r . . . t2 ' r?frr3 r +Eol)

) ( t+ss;\ )

o

+ +t+' . . ' t rSsrt3 ' ' " +(q)

)( l+ l?)

iet u.a iateqcr porj$'foO yq . 'r^€r v.f akai

^^d*&. -S ^'fi..

3'ga ) -a&. lo

Pcrlerv'a = 4t 't ) 3 ' l l t

, -O

@Ct p*+ 6r'+ tlxi t2r tt = ( t'+br f c)x{ t 6 rt+ l}r'+ lrr +|1 : (x'+ bir+c)(r'lbx1,a)

lc^di^gka^ pekcli r ' t6 = b+b16. 6

b"3 -@gendl l fca" pelal i xa : 13 = c +bt+ c

[^f ec," - - t3 @B"'.d;^gkar. pck4t; X :

8c^4;1La- gcbuloa lemdar

:

12 =t2:bc=

b.+bclbc(,

l f=c '

c'= l f 4

k.Ar l ,cg' 7c '6

T.1,,' bt ! , :: :s4eh *+ t 6r t t l3r '+ l>x t F ' (x ' t 3 x + z) '

Alabi la r$+6rt t l3* ' t t l l tT ' o

C*'t 3x tr) r r o

tr t r ) 'Crtr ; ' : o

l r -1r-2t- l r - l

hraha frrrreo,' pcrsrna,a,.. r++ 6ttt l]*t1

' l rFt | f : t rc, la l .L l=-2, -1, - l r - l

(br 6r+{fx3 -39r ' t .s-r t6 g o

6r. ' tsr -3t l +* +9x' z o

6(" '* i ) -s(x+*) -3E=o

Q.^t tka' , 5. t+ i .

r r r rke Ut.

* ' * | t '

T"i l 6(J ' -e) +sy- 38 = obq' i5r1 -5o =o

('15 t io) Q9-s2 -- o

5'ry ' *a" V'+Alet; la J=-t ,

x+*= -E3.4+ loxt3 =o

(3r+t)(r t3) =o/-o-) t x=- i

f la; ; le J={, T+*=€

c#:-,iiJ !,io,ox =! , *" ! ,

al.i gur.*t go-o.r"ro.o,. 6**tsr.r- 39yL4fx (L = o

aA' la; Xe-3r- l , I - , : -

>[?rn tqq+ k4,A,e

(9 t ' t '?ginrr is l ,n

" tzr;nf t

- :T.r-sir.- | + t

2 +n.nl- -"""--

tan i+t

- l+t '

hosr : kosr{-s i^t f

( t t

tor x i -!-9"Ir t '

3 s inr t l kocx=3 j O'SxSrto '

fto^tihr.r b=+-^t

3(+F)* ' ( i$)=36tt l ( , - t ' ) 3 3+3t '

Sf,r-bt I t = t>

{= 6}W. =: t" . , j "* . .*rOtoJ

* z o 'Z

0.2

t l .3 l ' , t r i l .3 l '

L2.6L'

Aoabita' l

.x+an 7

xz

F

{a." l,2'

*,.

)\

t .

Alab;ta

oni ?o'-c r

*

t : I

: eS' , t3S'= 1o'

t i^X 1 IkoS J( =3,

S t to '= ;-2-.6>' , .Lo'

tii) Kctak"'. frr; = t + kcrrxt * 2 JinxlJSaT

6o^*ika'. | = ta^f

Oleh lcerana O'-(

hpale;la t:O , fCt;

A?at i f^ t - - l , {C+1

z3+Vt-L"

-( (t -t1'-+J + t:=@'

x ( jo ' , naka o'S i , -( t+S'

9(+"f -4 Io ( t

- ( |

doqrt

=lI=T = I

3Nilc.i {'r;rtresa. fCxl i^t^L

ni ( a"' lcrbe.. | fu) i ̂ laA

e3J.3

D (-r,

[eecar,r.na,,, fyl : Mag =f+ ? *

-"3;.0:'_I::ffi=i.'. 49 se,lotr.i Clr . Dc .

beea166q. DA .. MeA =ffi =tr

tecqt/r^a.l\ eg : Mc.6 . -t-(1) . {

f4canwr'r46 Oq = Fecarkr\6r.h CB

D A sclar i dqn. 6 '9x^dn Abcs ialqJb y* s{iornlaf selcr;taccrvAa.r" De .ffi =#r+Laaga,.n r Ae

raec?.rura-a Dg x= ## = + = *'

9(t . s)

t iJ.e lPrn tqq+

Tlt;h P.nemloahaqi fgrq?nRik.^* nis b'^h I :

-Jko+3=t

| =12- l

pc"(=rJ ' r r"#+to --gf ; , 'Po ' eJFr

t... L.*.s A cPA = | t eo,t ( cr)

4Ctt = 3tr - ) t t

f cr t = r( t -x)

3C( ) =Kt-3xt>

3C^> = (x-r)(x-z)

grii !."f J = ft;) =P4. pa.ksi -x , )= o

# ' ) -zx

. xeR3).- x- 'x ( r -x) I* r (a-x) so

Fso , Ft3

(+Uf r"ratsih^u'.)

:" ri+if (+ , + ) ,^t ̂r.+.iliF w.eF:inum

.x,

.Yt

;X

e1Re'iR

eR.

A?cbi l " * =o ) t - t : = i

! i . = -r .<o4*'

&g.brt f F=i ,S=t

rad, 'pt"#,f fJ=rG,+)

Frcrunar. Pq -- ? -I:) = + = #€ -(-+) 4

.'. Pers*^".a. Pq ia,toA

Y'+ = i* ( , -E)ot-r fo: r t (sx- lz)' toJ = 55x+61

Pereqt..-n 90, ide!, 5lx -5oy ! 61 , o

Jarck teqak l r r rus dr. { i f i f r Z(E,-z) kzoal'r's Pd fa,lahgo"i.t

- Pd falah =ffi=ol'-,F

g1i t'"t y = 3(r) ' rL- 3x t2 s(x'r)(r-r);Pa I g^i's,r

' -l , i;; + cr't) ct- L) o o

F: l r 1r . : L l t tn crcs 6h,r^

?,, r . r_3Apobifa f t ,o,r -z- l -

# = 2 > O C++ih rt.irs.r"-)

hlobila *'t, ,.J, '+ q Tfl,k (i,- i l idtJ1il;b tninit*trt+ ,

fc l .pcksi-) ,Fe6 9,y=.Lelora^ tr^f fcr ) = 3_^ -x'; f, e& ao.l

J(*) .

^ ' - } r tz. xeR

^da.lal s;7crh be,n'lt',* '

5= g(*) . r t -3r f r - r . r€R

y.{a)=3r ' , r r ; xER

I

(i' $l

( i ,* l

(r) hcr). ta (rx-r . ) + Fff i0lcL korona h x ha,.q6 +cr{..&r:i{. ,A+r7o , p.ft- bali I,i( gx-x') +a+arrif ,

3x-x3')or ( 3-r) ) o

. . . B^?J x (3-x) )o,tut:b ln (lr -x') ha-y^

o (x(3Ip.^"1s.' :

JF-3.r, :

5.Ai ( r r ) ( r -a)>o

( r -l) - -. o-l-gs-+ r {+

( x-z)

tvtalc^n f*^6r;-fr6 ha*go. fc'fa,rr,rf tlnX< | a.{z"aa'x > Z

I.4i $,^tri hG) -- l^( ax -r') + #trr1".ui1 u1; {x lo <r ,El n [r f * , . , , ,>.1

reR

T"dn O(r< r o{or,r zcX(3

i. Ba2i h(r) = r^Cil'l - ftfr

+cr+"*dt ,21r.3 1 .

@( ir)

ft3a.lcila daq

#=o

Aao ,

*?o r

;. Tecda?*t '+i+i k

fd. t "€k*^3

9a1i Ie^gL,. j

, -$x = o 1

^=o" l3g - t

f f i = -6tF o

5= t , ,

t rgkok b<Jas (ot t r )

J =- 12. -x,5 .

- l2-9f o l*rul :1r-(31o

"i;!l,.'t ' v

Ora{ f<.5e : 5= lc (r)

Ago't': ta

Apabitq

vrs

h.d k(r) = had ll*-*'l : or+3 rt3'

hcd Strt = ho,d ( x"- l*t : ) = 2

a13+ x+ 3r

t2-+x= [L-^t 4

t ! -+x13-qr = o

Maha hc.d {qp; f had fCr) , 4t" i.|r,x-t3- ' ' t3+

' !

|f, +" ) tf4@F w*J' el J'a' sotcrusw.-Jc

F+iA4t' rcto'1)an dj +t+ik' lr'?

hed FtF) = ha4 l r r -^ ' l = L^d -(3r-r ' )=6t - ' o- *- lo- r+o'

hJ k(*) = hr.J. I t*-" ' l = had^ (3x-r ' )=sx+oi

' x+o*r

- i tot

... t"a,d ,eG) = h^d h(r) g oF-to ' r JOt

T'4i h^i l. Cr) ' et-) o

Iuga 1al , ;h Aeo , k(o) alol=o

cle-t Fcrana 'hod b(r) wuJwct cLar lg"

Ftr l = l .Co), n alo. k -r ta l .A

Seta'^jer '[i liltls 'r

= o

olaLi fa x++FU' t2 -x3

, , != -&, 1s

t€

g*A; S.. f Sads rt^rus 9= lupe. pa+si -* ,9=o 2 x=3

ia. 'pef .s, ' -g, x =o P 3= lz

S"f Sad s tucus g= 12-kX,fa. t i la

x 4 -cr

(0, trt

lrf )

ct& o

Ag

= r [+ -e6-=r({p)=

x(t ' - t+) = or(r t ! ) ( t -2)= oxior x.-a , Xt2

i la t1=o t I t lz

lnpal,nt boykaA b'rarwr &' r'arrfrrr I

UJ ' J',- " ( y,'- 9,') dy

' .J], [ t , , - Tr) ' - ( ,r . x3) "J ^,

'T J-n (e+xt+l6rt- r ' - isx) Ar

=n(6^F+ '+ -+ -trs^'J:-' n [ -Cqe- + +$ -rr,)J'' n (qs+#) = W.1 tr z t>o.Vu n;+3 -

t.t*".t* llFad,rr tet\atat , =ri;Ji,l.O,= l f zr ui l r .

APabrta Ag -2 , 9t 1r ' + 8 = LO

Airobi ta K :2 , 5 ' ( ' -6 3 +

i. Foo"Air.'at +t{'iF " persita..3"'a( -Zr 2,o) , ( t ,

4 t.yk*

P-dr,lffi

)

)3 -Gr

= -6

f

, i f4-6r$-

tltpaA,r lonftrAlciraraA &. netAr A

v' 'J ln(y l -g, ' ) ' t r

t,,.-*t = ,r-J.t (r3-l+*r-t5xa11e r)4r

r{as A

t ,=[e-t?tr

S- t'^'J'$ t,r ' ]=n(ro-ff)Tt.6 n u^i l t .

lc.tel. (o,tr),

I(EoAH "OohGriven that the rnatcix A it s\ngutqrrwhcre

+he possib\e va\ues o{ . E t+Jo" (i, I -iil,$in4

ilisr-f G

+".ggf : tAl =O $t.{.d,l-d,, 1i:t tz* 4rqo(r

*r l i - l =O

t f-n-(-rra)] - I I tl 1: 1"].* : I q"- zJ =0,/I fZ + l lA - 2. t+A + t+4* 4r*2 = o

or 'o

IO and 3 ,*u'

scluafe o{ *he grprQgsioni i r <Z,IA.Wi{hsutt {7 , dqdute, rhat 5Ji + aG < tt} t61

S1ggc:1ffi[, +,fd]E,)r a+b+2/f f iBJZTE+^-b2e + 22a + 2 f r , f . ' . r .@f

la= Itet a=rrQ ,Fcorn Q

dl- t3a+ ?O =(a- to)(q- B) =e= tO ) 6= 7

.'. Po ssi llg vatu€s o { a ar€

--

--a

-

grhe {unrtion + is de{iael

$I3g ocbcab>ob" >o

-bl < O g'

- 41- br( aa{az-bz ( A

--r2/at-ba < 2a2a+1at/

Sub sti+ ut€

,,68+.fi.6 <,rGa/a:IG+/FE < tJa ....Oi

bg { t r - l2x- l lt ( r - t ) r

gncet $ sei o{

++++

1z/[fr ,./2 (")

l+l+ 4/

t-,l 2

a

, l, t

III

I lc(2

x >l .valueg of xSketch the graph o{ f . H

sushtho,\ l f t r ) - l l *2.

c6

r6 l

@gg$f, ftr) =

- lr l

/

I2r- l2r(- t l[ t* ( r - r )

, x 32r I >2

32s2

r( Look qt fhe, gcanh wher?*hq c aa3€, ot- g" i 3 to et n,€en-t and ?.

So Se+ s{ valug o[ x

, [x,o-<r<31*/

,/

- \

(r)

[ { txr-2-($()d

- l s {

5

32

I

- t Ig: [ t r )

-

&nsuleci J(r +2hr( + kr+ 2k-S =O

_-. i a.+pa1 cf.A_ 20(g

t(kl+rk-s) g at)f+Sk 3 + i=$k'-2F.- r+k+to t\- 2 q'

i:'iliT-i.l l3o -ol#ni t2[kt-2kJ +lO ' v

'l .

5o da+pa> to{ 2 circleg whic,h *ouch€s {h€ tt-ot(ilr y-ar1Sllre goial ( * r2). 8?t

- f - . - - la i r=to

,al ct,.- ie2+ 9a-2o[-log t f og--

l6 'Er+c2+ t+-trr+farf 1 ! r= 2r1-12r+ro co iT[=l ]2+(u-t)?=22

( . -10)(r- l ) =o'- i * . tg._hr_Tg+T=Ors fO t (=2 u- e- i - 't

G)F,nd-, i^ terrs o{ a,- Fiad a\So +he least

'n-ust be taken SuGhog +ha Surn o$ +hlg

4 a sw cr, First l1ea, 4 = ICornnca r6tror ?= +

Nu,rrber of te,rmsr N = n*ia(r-cN)

l - f

thc sun of *he sQ,riesauartoGc o$ ttrarg a$ +h+t^fit thl' Sue'r s{ *hQ, 'sqcics to iafinitg. E?l

5N=

l -

e 3[ t _

5oo= *

= 3u,

Sru :

Qt- l = 1+Tq-r

er_3_l+g-rs etvlul{ie tr1 b9 Q-f, :- (gt)l-3 qx- $ = 0

lg rvl

nna-B1vr_11 =O(9,- l+)(-+l)=O

--- ' -n=b ; t r r : - lOn: lr, er, -f

g>o .'. er o h)ta loJ3 t+

I'= la I+ v/

i.o.O,; g= g\n$-t = 3?out oQ ia{erscstlon( lnh, 3)(a lnl, 3)

O. O0ol

ro9 o.oool > l3J(it ̂+t r'.- + ) (n+u tog (B)- + > (n + l l (- o.[16oq)

11.?t 5

I

I

I

I

I

t

a

t

t

I

t

i

I

t

t

; TheI

:u{ccn {t,c cufvQS u= &l and+hQ c tosed cgqioa bounde.ol b,a+he rrqr{ vatuE o{ +tre arca R.- c4l

9re cr- 1

- 9r: f(t +f e'r J_311 .

-J,O'

Areao*= J u ?.qr + rd *) ,lxt^ll(r+ + q,-') olx

=[2f(r I ]C*U {a4

=[.(r"qJ- + c,j:r^hJ- [o- $1:2 lah+3 ,^, \ i l r t - "?

i^..o9= Jj^hg*-r;d*i = [e*-x,Jt^+i . (?**- r^ +) - (ec-. . I 7- l" l t - ui i t t

:9hotlcdI

t

a

I

I

I

t

II

octq: Area A- 4ru,a8: 2lalt +3 -j + t^ * ,--3 7la+ v3 3tr la))B 6 fa t re^-,i L.

S*sWggl g 3 Qf,-l .",-.F I

g-- ?(i+r{x) ..Y@ i

$l!ggf: :^I'AfrCrrrrrrpl . ii tc{ j ' l r r ,gr)

p (tp., $p) i oK-#i+lt j,.'P.lo.l _g.=8x ,?( = 2p2 :..,..Q : l\(a:

'rjtr-:ux ',t'

93IFp.. . . . .@ icois ld i r U-t . . . i iaal t

) rg 2(*)r . - iT; . T, v

iJ l ,=tF(P+t l

t

^ . . ^ |

-PnL=-l \ - / f ,B $aZ3te

-v ' t iCcnliderl 'coerdiaote1, (Pt- l ) ,

O f+ is glfur I

ffi t ̂ ad {he integret Jt{try dr is

rulqrwilh the intqrvalr of wid{h 0.15, fi"drlal,ee o{ I , 6ivir3 lour arrrwcr corrcc{ a: 1 d-.p:

dit Cg oQ,aat c{ rubst',trrtioa ff,= u-l r Show f C+t" t i-girtea bg t(l-G). S5l!

: 3\- t

!s: t= J j { t l rdx

= O.?qX (3d.g.1 . - -

a^ urrSlr l r -

l-

Mid goiat o( =c{tid poi'rt P C,

qo f i=u-r . ."o [ t{ .rv6* =f 6.d*

i i=#dl s z,/-x duai = 2(u-r) du . . .@r-[i^it:ETrF.o-@u=21 . . .r ro, Fro-@u=I J" =2{g6-2G

-EI

!l

A(e+ rXr-x,)+ b(r-r)+ C(z+r11t=- ! i^{o@ : B=-1, /?(,s 1 into@: C= | , , /13,O iato@: A=2,. /

i A(e+rXr-r)+ B(r-r) + C (rtr)a

(2+rtz ( t -x)

.....@)

? ttFf- ia par{iat {rartioas. trrl@

Express {tr} = ffi r7r partiat trat

,...,a,^Aa.r.^,.ccadiaj pouerg of * uptothe si{ cf valuei of x

Aa-

2tx

1+ 3r-r(1 =Subs{itu{ eSub slit.rt CSutogtit ta.

... {c* y 32, ' | - '(2+r)z(r-x! 2 +t(

I

(3*)*i(, . i ii t l +t ' t) ( r_f +...... ]

I.1l

=3-lLrx, ta

! -* , -#-$*. . ' . t l

"' f(rr = (i - f.* l.*...) -( *. - f; * "') + (-* - ir-h *..)**- f l+ *

Fr garsioa L^ q -!--

v , i erpaaSion t vefid .1+r lrrX)r

l3- l z l \ - r^ '

i l - r* l< l

' ,1*,. , i *r. f

t r , l >z ! l l f>f) r t - )or l>2 u/ : XG-l c? X>l l - -

{tr) i I vc.t id; Sqt:

I f t l r ( -1or r)

I t' L t-t t '-D

*' * "" L--

-?T]'i)= -r*(r-r")= - t*[i* (-r)(-r*) * (il#$(- t*)t*..,.]

+ tx3+ a,gt+ bx, - 6O tnal a 4a4ortd bq (rt+3) thc rQaaiadcr is 60,t Bl - shcw that (r-3) i l q

4qctor of g(xl ard $i"d {he po0 (x) = (r+1)(r-3) q,(l) . t l+ lhq,J( ar,J fect. roet3 a^d, fi,n,Fhigh p()c) > O. [5 J . p(f , ) : (r+31 Atareiaderc6o

i . ' . P (- 7 l = ̂ 6o IiFrj** iel tt+q('3)t*b(* l-60=60

4a-1b-6O=Or'. b c 1€; - 30 ......r@ '/

Egs) b:t(rl-3o = - 28 ,/

L^ t!fSCc{iot :

* 111-28X- 60

'* tltl 2E(t)- 60.'. (x-3) is

^ factor oQ' p(r

p(tt) = (r+r)( I- 31 1tr1: (x+r l ( t -?) ( l t+ 3)t+ lo)

... ,1,(r! = )Cr+ 3r+ l0 /

- ' - a . | . | | I a . a I a a a a I a . a a a a a a a

{(r) = OItz+ 3x+ fQ = O-)

3 91- h4Cs 3a- tr(r l trog -3t ( (o,

P(r): (l+r!(r-a a a a a a a a a aa a aa a a aa ar a

Co'r^ p tetia5 Slor€

f ( r )e l t l +3x+tOs (x* e)'_(I)h3 (r* l ) .* #

i tet gs{(r1l

Sgn theH cth x lt1{ -?,

Division1

'.' ,to

- l t -60-z

,(

to

ol7q

-307o

(>o)naot h c,,

B*t

P(r) > o(r+1)( r-31 t(r) > o

q(r l >ov - . ' . ( )c+ l )CI-31 > At/Sef: t* 'X(-2 c? x>?I/

x-r(-1)- , 9)-0( lXr(- t r )+ , Ud-o()

Lf -0O g{ II

A.frBg SrCg to-

$txl: o 4o€ tcQql roo*S.

AaSwGf:

I . Statc +he eluotioas of +h((eS. f 1l Fi"rl {hC csordiaateslqraritQ i.f it iS a

^rcxithu,u or

a ariaiaaur. po!a{. t 6 J Stcq*eh +he graph o.[ y:ftr). C3JUSc Sour gcagh *o_{iad the sct _of valucr of t< s..ih +ho+ +hC€tr* a*ioa lc(lr+ ))z- x = o ha3 2 poti*i.le dittinc,t coo{s.r t lI

)c g -2 i i e^ c = (rt+r;z[rJ_ ,

,9{ I - - - ' ; ; l : : : ;[(xt])z f -

( I+) I?

) t ' .+0O . 94

trrI

.2,

I

IIIII

=?;k* [ t

2- l = O)(eZ ,./

k(xr 2)1 - l tk( t+1)z

k

ak =

2k+ | =

The goia{ (2, Z*l isA ac.Xi(\var poia{ .

I'rltrsc.fi,or, ,.,i+h otat ') tgO , g= t

5:O t l t=-o '1 Lbr ls-$ '236D t"a bt r

-

5 5 b \ r b \ \ t 5 \ t t

Sketc,h {'he. 6ra$ g= rlctt ,,/Frar. *he gra?h,r

- ^. - jt<5<fr

IO1

set, [ r ,o<k<i l , . /I t i I r I t | | t | | t r I I a

lb.:l

' 'J= 3!31-+l s +(z+1lr +

/ur'aXia^va