eU$"-- 1'I

ri)
\=/ J (p, , t") pp5d".ncc L)r ,-xt ). + (?,-'A ,"

(*,?) I *,dpoln* X'+Xy Y,+$e\I

fi)
\_-,/ i
I
M ,}
L/

@ hnuq = {, (Baz)x ($.int^+)

@ PdU-1aoYi€*, TLqo
'o{rn

Bao\ I
 .
trase -
l-
P,.+ +t.
+-* se{
s l
l5 q r?ea I Tturn

:h-$;
(3,1)

rt)
tz,-1) 1
('r.4)'. a-=a ,
fr*Ui

lr
g" i"-l-s .,,ilt be- ol1 a r.rcG-fi ool t tn? +h*f rza
r(d

L.{n I
o*t5 '
$'-

J?- sc (.1

di:-tr*nea d G, pr) t*!rv*o*, _l-fu- ,t

Fo*n+E
,

@ lt
l.
'i t B(e,r)

,', d (p, ,?r) = (o-z)t+ (0{)L

.1l l-t i.

'i,.,

::;liel.
 -.l

fr{E,!}

j' d (1,P, = (-r- -e) z+ (t-z3z

I

=Jm
*
=fi6
CL"u
IL
ts

*:&
f,
@ E= (a-t); %= (5,4)
il
F

d (n, Pr) 3 (s-s71'91-r)'

2 16e
:i
ir.
I
\+ t7 .lA
l !8"
I

=2.{B-
Q+,*:)

@t = ({ ,-B) ;
p1= (t,z)

J(pr, ?1) = (a-t)'+ t3-2)"

1
J4+zs
Jr?
(*'t
L_
 d (P,,pr) *ej'+ -f
too * 25

{trs ...

= $5f
&'*
(c,q) (o' o)
?L
; P. =

d (Pr ,?.) = { (*-r)' I (a-o;a

I

J""+ q" I

-j

@' r)

l
 3t- 3L T" P.,roblc*s ?l-g{ ) plo* eqek po tv,{- c^r'd S*o- l&r-
-lnian6Je Age , Slant +h.+ +t^* *nron6t*.. ni (u+-
.{,too
(i
LL, Fl"d ,*s qr?eq,

A=Qz,S)r 6= (r,:);
i
{
i
! I c= (-t,o)

E. ]1
til

ut)
!,

*
*
t
c 1-

AB= (r+z)a + t3-s)z = {g*" =JE

e e. = -l G*D'+ (3-o;a Jt+? {tg
BC= (-z+r)'+ (s-o)L j"A
-[G.$

6$ Bcz = A82+ gcl

Bq =J[m f +NiT)'
13+13

{ {i,

.I
u't % -lah+ toi""6tr

).
 1

trt**+r(t+eigr.+;
t_
= t?a .lrg x -[rp

equama nr',i15
f
&s:]

A= t(,8)i B= (3, ; c= kt,s)

c(*r
& (-6,
r--l-
AB =l ts-a)z+ (e+s)L =
j et+ 9.1 = .l tqs
{s,-*}
L6+ t)'+ (3-s)z = J zs+et ffi- {_3

8g= (3fi)e+ (-s-:l = t(+ too ; rr].b i

-; ;.:G
s-\ i.l

3{ r""
t: Jh__

.'* ABt= &(2+Bcz 2lff-

Ao : (.[tfr'+ Q.r6r

2? + (+ rz:)

= Je+rra
$ rEs tiqt * +"le"AE"

A*e^=
+x (Bere} x ftt-a;2h+)
l
=;x
{ dtY XZ . Ia:*r

: #x (,1'E )L
-E*
a& S1*qloe. ,.r-*,i*>"
k4*,;
 'a .,

(1,-s); s )
1
q
= (*,1) " l3o
zlj"
S

fta
_r+t (1-?)a+(-3{)2 Y
.'.'.

8(: u- z;1+ (u-g' = 1l- " {

B(q,t)
ft& = J g-,r)"+ bl-r, . 17= t + ({,-r)
I
T
A

aa
$ 2-
k* + Dc' I

,4< : 2z+ 4t
= Jt+ri
=JU
= 2-lS

5a ,+ is q railr^f &ia,'nqt*-

/nru,, =*l (uase) x (He;6r^+)

=Lv fi/> I
l
.t
t)I €uavQ_ uLrart!
(4nr*

l
 'Tt:'t
Ivt f laob
Ynl d Pe rrFf )I
L
n|
Fe in+; Pl
al +1",e-
a "ft. or.td Pa.
:

= 'i (r, o7'

4%r

t qi** i
3i ?.. (1, 2)

,Y (s,, P-i ( a.+t

r
or
* 3+a\
%
\ )
\4"Lt
--/

(e J t\
zJ
&{
Pr= (e,z)

- t+a -3+2 I
I,4 (Pa,Pd
= ( rT- ) t- l. -1\
r
?^/
&'
"-€$ Q = (*, e); ?:, (o,o)
(
a+o
L ,?(n+-0
):G, g\z/
A-
EE-
-

@rf'tu p*i*}'(3;8)'is s[,St"d'e €n lL -l.

anJ t *ri$l Jowvr, r^r !.*t 4roA "r+* Yq1^J coovud ?

Y
-/ t !*,\
{ ':.rq z- V*Li tJi
\G| ) s
. (9,,1)

.'. ,o +^* vrt:^, .rrorol'r vlal-a5

artyL tsr,
4,,,,

69 (-t,a) ?s, sh;F+.d ,' '€ .-i*s {= +l"L bs

and t t y;i|, trp: r^:!rc.| qrd<* Ll9 , -l r_ coonJl"-{<., o

T
+ l+r,,)
(-t19 (-t-z rle)

= C9'Io)

}h* h4-!,,r cooY,f it gl+

\
'A'nr'.

>.
 1

.!\rn
r(ii nt9
po hav r rrgn 4 )1 T- cdo Yb d i ***e- +
:\1
I'
l*anc{-
'-. -: ': : \ : i'''
-r

+ ::

&t,23" r{f
t
I

I t
a
I
I

I
I

Le+5 l"f.flqqr\nq-
q i5 ?,
fi = g*,a)
P. = (*:3)
IO= fh-$*+ S-$'
+ to?x 6q + (z-E)'

* , toa.. SQ = La-*)'
+ *c = €-AP

? 34,; (U-*>'
i-t = t,m-
? ?=ztg
: e*4 oY,a ?, : a-_[
:$ - = -\

(t, a) qnd k,.q)

&r
 po
I

'fiE, '# -4
D,oJino'fe.
arhsae- d i>4*nce- -F** Dal nI (r, a; i:
I
t
E

(": BA usiv'1 +4 Pflh-(.orcan thedvla.yrlr

(a) ,Ot asinn +h& d irionce -[or**1. ,

1
+
. (tr2

.}..

t-e.ls inraqne +^^+ *-rooraiinqL- 1+,s-poinJ i2 x._

P, = (r,z)
ltr= O-x)t+ (z+e)' P.=(tr-e)
+ rFz: (r-xJ. + 6t "

) q s?-al = lt-'x-) L
) (t-t;}=. Q{$
+ Y*t: t&t;
? t=-1"tr5
1(:--t+t$ 6Yl A=-L-15
jcl =
_tq

(tr ,-e) a'"a, k,q ,-a)

A*,
 @ Fir.d 4ll po inlS o n -{+,8- r-- exi5 +\*+ aft€. Ie L.A R
I
1

-}l'!- p,,ini- (s,-e).

i

)
?=o t'

Lalg ;r-n*tlng- *.- esot3 d i,',ete; ,{ +Lq- 3

fr> n$,
I >
!,

P, = (so-e)
,to *. t+i:G-o)' F* = tt,O)
ll-
G-ro)

? t? 1 = (s-x).+ gL +r,ti. S*&.;" *

+ tqt -16 = (.'c-s)l

? to& =(x=sle
? z-S =tfiffi
+ 1(: St.friis'
!
?t: $- f.-"-

(s+'lrrE, o) .*,t (s-tTo[,a)

t
ff+g

-t
rl
rl @ trinJ oll ooin! *?1 J{"e*
6 - axi>
+nq} qne G
t"ni*s S*"n +!^s_ p*inl- (1,-g).
:) .t. x=o
Le+1 , i"na6;-t*- eCIonrdlq{n r # +.- p.l,rt, ,t .t}
A.- B

,', q =(qr-3)
($-r)'+ Cgr.fr)" f.= (o r 7)

+ 62 = Le '+ (X+:*)L
:) 3( - t( = tt+ a)'
?+S= tm
:) ?= -?t{eo

(0, -s+Ja" ) *^d tor-?-i-*)

tu,,

r'
 r

A'.:
C u E
l,.r Ir \
::;
i \:+ t:

'r,| -f;' *:
(
lq
1,.

'' ,t 'a'!!:

11*fr rft - k i"us{€-d o# x

r
t,
iF ++,'r-- {Xw-alt ow J" ylel
iS rA.^*rs*-|n;e* q&:ou__{- -i-\A_ rJ

v*-
l,
I
\
!

\.{. , I t,-)r.n e*+t'tq b"o-+ *f^o-

^
a
$

rI ed .L
-tr I ts::.: al
-

{ t,q e-1,,-"*{i t, 6 do r""+ ._]Ln-n +t-k_-

(nqtltl
t5 s!$ rnrne.-i"r'r,q .nbo.r_* +1**"
( x-^F!: "

@ 5E;x-e.d-, Dl"li th,

;\
P{? ;"., *1r i n5*cJ !h,
.n
+-4d o*'
X -{
r
I .n
"*re

t) t-?- { t"q_

ff*rh 15 .>trh*eln ic- a&oo** *

I

Q
h.a-_ sYti vt
 Qeneise' L'tua{kn-- t'L
g?- lg
T- Prroblor*s 13 - lK , de-*e'o lm; ha wh ic\ +r* r€r
"$ AI
po in*s QYa4_ 6 n +\"s-
fi*o [h J +u. e1u,r*r on

E1,^"*bvr: Jl.
t= 1d_

%lnls (o,o); (r,D;(a,t)

:i,_l

# tso *l h*n
f,= o
lt x= I B}
a: (l

11 X=z
[: ffi- JT

&i:, (o,o; ig oa- t*

tfrph,.
€, f,u,,*rro h lr
l,
t?,: 1c+-t

=) a=?
?,
I

P";''i: : ([, L) i (o, r); tr,o)

t!

''f ?=t *ur"

\,F
Lr-
l!
t-)
|
K,, o'

I
l) Ll
d eO t| ?t'=.*t

t
tt
F
tu (*rr) o^*d bt,o) aY..ll(_ on +!-,L 6raayh;

I
 t
.rf +4At't
@) f1*o{o':
.i
6L
t xz= t- I
4 !

:) rl*: S-,?"
P.;'.,{> ; (o, i), ; U,o) ; (a ' :)

u-l it^ -(-= o

d-r it\{I:

)i r-l* rl
\
v=L
|1 Lr- ! r! .)t: r;
(- 2-

&xa: a^ & (r ,o) ouYt'c- ot'*i"^- (-I?nA P h ,

3?- ss T" ?*o}lamg [?-30, $)"+ {r^- ir,krr..egl> -r. d Y$4 ph

: a
ea*h e1^a,$a.n bt pl"*h"6l p";n!, W SL,LYIE* -l= loL e[

+* in*e"rc<p*s,
YI

@ ? r?(-6 -_ _,..- .ri_ l

=) l; n*+ rt- in*en*f+ "

((po)
5** ,
i=o'
O= lt- L I
t

) y-=L ((ro) I
I
I

6- inlen c*p+
,o
€
1e* x..= o
f,= o-6
+ ?=-A (ur*e )
a
V_--

€* t= 3,.-7 Y

in*.a.n".?+
.lu
fr*+ r-
Su* Z- a E,o)
o; 31:.? F
.- I
?,
=) 3X-= c(,/
g,o) {u,- ?}
+ 1t_
= ? (

T" # 3-
ln*an ,n-pl

5* *=CI
-?
?= Qno)
:) E=-7 Lo-?)

'& = 'tt- L ti.

X
-To
# rr-inlcn.epl
*a* ?E€
x"
r
t
i.

(or'D
? 1tZ= L

+ t=tr ,'.("1,o),(-',0

-1o i"t<-n ,.e?f

?4.1* tr-
s** L=a
?=o-l
+ l=-t- Lo,-L)

t-
 I

x2+-l
d-
lc
f rt-i''*en.-Pt- -t
.l-
.i
: l,-
:

5& t=t
,T, +1 Arl )
:

=) Xat= ! rn

=) r= t1 tr ,o), Cl ,o)
--j

-To
Xa* q- i"*ancept
I
I

iL+ tc; o

t: o {.-l
E= r

ir 5r.-+ 2 I i,,
Y,
-To
Xa-+ x- in*arrcepf
,I ar]
a"

5x{axo-) -- lO to rS)

+ ?t:, t* ,'r Clro;

l, *)

lo qa+ A - in{e S{a F+

sa* x.= o
lspo)+ 2p =1o

* a's (o, s)

t- _/
 @ 4*+X,\
n."+ f-
-To in*e"*++ Y

s* -fo' '

4t+a-\ P,q)
(-r, lro)
''xz= I
+
+ 1=!!- ( t, o), (-t , o)

Io $ intcroeepl-
t-
,a-+ x= t:

l4t o) +t=4
+ 7=1 1",1)

fi+ eaek g*L*F . Jh*-,,t pfn& +-*{

3f-40;
P"
i+f d+.*+ ,ff*rrrslw, c + l'l- wi+1l ,re+pe-e{-. 4-
rJ

(a) -l+,s- r-axi;,; tb) +!',l.- ?- ^ri); (c) lu enlXi",

(o,t)
@ tY
Y- Qr,r)
i
T .r- " b,a) q
5tr*' oVo?, = (g r*ar)
-lt^a ,6- aPtS "l*r*f+'
.H
v
b = Qa,t)
' (3'-tt
oril C = C3,-q)
j.r aA-. o,bout

3;inrneJnie aba,.| +u ax5

t "c-
F
i
-fte onl6in :

,i

il-

r
 (t,-z;
,Awr-T[*,#
r vn. abe*l{tne di: elu]
-Gq', r)' x- api5
l- 'b
= (-tr-3i
G
(aix) a
L -- {*t ,t\
\ l2*t
-*f-q'-?)
'l
d
3{"m: abnk-l'ite
aoui.:
?*

, cr,-r)
.1 a; Gtrl)
4: (-r1r). . (t,t)=c b = (t,-';
ttt,-,)" r ;.-i) = b e: Lt,l)
i.
I
I

1
t

,!

,E
(t,o) r1 tg pi "Q4 inr{ad
erE?) 6 "(4'o) o* i") -l-o *nd
(+ ro) +h& 6A-, abou* +-hJq
x
(o ,o" ,:3.:) . =t4 r oJ ?-axis,
r pl? inf 1i) i"s{ud
# tt: e -Find +i"q
qb*t,-* -* hi.-
fto,.
Gs,a) rt- crXif .

F fl? i" -:r- in*{*J

a:4-3,o) qr{Sr*} otx &nJ -X l*r"r{ed
(-a.) b:(
** -find *xa*
! 5 t{Yl1 , abaur* +v\&-
I
d

fi-axis-

L
 ,t r :

1i
" l- .-")
JK - Book
I

4",g, \ije ??: G t] e l-i yi o in -{+,g L,

I
a7-n Jn PnoblernS $7-72, li>+ -h,( i"hn".p*r .rynd *.s* $r, ,At.me{a#.

i
I
) tc = ?"-7 11
L
;t ?
t
t
oa I t1 -lc ir9*z'd oJ-
:i
Ta :Fi" J *r^r- 7 -i n'Fer.r
".pl
5c- tr-*
o '" -ft" -*7
rr.= o-) nrr+ ,lYqyrte-lr..ic oboul {k-*
t (
?qc= -7 C:,o) 6-orzci2 A
_Io
4*d {i^c.- - i nlero.z?t F'
-? )" -t ivu*.J #",
6
l* L:o
'. CA)' - I-+7

o:aw7 =)a =x*7

? 7"=z lA * "nztn ic abo,-**'{+ox-

x -axiS,
+ t=tQ
,n . (" , 3)
"*a to,-3)
Y
l *? i:a -)L i,rr'l.J # r
bl (-?,o) ,ta,3J, to,-?) ;
-t rl "a-
5A*. qbL,*+k- ;*-qXi: .
.^. ta)1= -?(+?
+ A"= -)dS
@ rTmmelnie- &oof
-+^a- oval1io . @
 Tljtn -1( ln;,{*e.d
"{
,a-
*x= -j s
@6= .Y

ry+ s6*r me*nl c- .,tb. *+ {r.*_

*/
-\ ,v - 'o$
'\- { 6-axis. O
--l; $"d -r #p
:&*,"e ts*ivt1e.reu-u_pF r1 fr 'tn v,1tia
_ge* t3
<lt =

"{= G5

+ ? =G , '. q*r&) he,-t-

t

.rr * &t{li (
-ta -Fi** 4v** g-ln-ieru*ep t
!

?f*a iyr - l. tn*1ed

"tt,
y-
S* ?:.* -
ll
" - t rr' ?
ffS'* -x: ( I,?I"
(o'') +)x" _ ? t
? ;i*o =), x,. ?.S e
: -'., (c,*)l $6et , **
*trvts* 6n c ft-rn
+b*o& m"ndni e. qLo + ke" s Yar$ rn .

*t+A - ? 'o
+ ?= 9-)L2'

lo *rrd. +).a- x- in{cn*opF

i* t=c;
e:?-x*
* xl;)
* 1=tS ,'. (g'ole*d{.*3r$
T€" & nd, -{ ur- 5e*. g'bae* *t.r--
ivr*ara **
3- p{*
ss+ ?i '- {,- *- ^xig,
H-a
6* I (o,U
rq

t** *:z
q, =tl

'1

-Io $'.,d +k- p-infen

I a+- L4
(-
;
:I

7 xz+o. =el
7 t?.** 1:
;i
. + 1q=tl
n, lro)
n C an^rd Gt,9
n
-To *inJ. ,-l hc--
' Z_in*cncapi-
5e* llc;5
(rt,xo) +-?t= t
+ u=ta
F*
L* ,'"J ,-,^d (u ,-)

,4w I
(r, o;, C- l , o)t La ,z), tor- 2)_j

ft
vn"ne*" ie q.bo*+ +r^< l-6,.,J,
t4i5 .^*,
^!
o',i€li"

I
 t
9 Hi x'-!

-To 'S',d \
t
ea"n**
rc
tl3 r -:t
3€rF g=CI

Li
)t'-,

nr
!o , -lirrJ :Jt^a- t
tR*eltc-+.***
;-
\I]

Te+ :c;-o

t=u-l
r)
5**;
'' (olr*r d-*, (rr*); Lt na1,(or-* F?*, ab,r.g_+l^& tlls.
) t
€ry H
v
r?t
1A J'rra +h* I - in*o,rt.ep*
4+- r{+{}
(
E
&i i-
S =td'+'*i
+ *--1
Y.-
* x: f .l-ft
"Ift.o jx _ irrkn c€pt-

A*: b ' 7) a6o;*{r*-

" 'I"l t-*'}.
. (a?
E
 u tt pl Af i n -rc tvu-$"e-d "#-rC
ri
[,
F,
iiii
-*
v 21(
6-
(=5-
-tL-x)
to Srt .;L -lra_ t n*en o.p{*
rr-
ta? 4
sa* ?* g
- 2l-
ato** * t r*
&q ean'^
A<e\int'5
elt
pt? It .--2, l*llad S.?*
? 1tL = 7-t
1( -'l
? rt =t?- d L)L A
@-
rd u{* ta,** 4+,\s.--
T" Snd *t"s-. l rt lene"c p c. ?c--a-i, f 5 ,

pl*k ly1 -"lL its}ed C

r
5e* \(

+i oLt tt tL -? rt r!

*
2va t'd :1.-
- [ dorrorn iuq*d ra t: zav*fi
t = 2bg

'(
1L d,+

[*,.,J*S dJ
"* -Lq
dI
) ?r,. a{
T-L
+e

A"r,i (2,.) , Cz ,o) ,

.!6tnrone*n :c aba-.c{*" \,/

-++,.!-- at-li r! rY? r

sH**- qboo**-l !as- o-a;i ,* It h
t
I

jj:=-j.}.#.

I
 -I.tH
I

r .-tr f'n *v' ir*,*4*J 6-ts

tL
-t -!_
kxJ'+ t
V-tn -fe \"e-€ p!l ?
l-
.-:-'..d -t-ka.
2b*e}s
jer ?= o
!

n--
r.-tn.t I
xt+l' .'
v *? xl &
Zxs
tr$+' 3t t'l .r* *us* t-*[i ",**.1
I
+?-d #y'
!:\
' '
i :l
--'
?l:a tn -d !t rn-}

4
)L'+ I
- Tr,rtsn e.rta*ert (,J an ortivrehyQ -a 2xs
c S. a -f uo*
t- io 1.r..p{- #
se-l L= c: ,,, ' tq wl. *kotsf '4'he- x*axi:

I=
,L
q+t
Fl."0. rh -Y* i"*4eJ
I
#* I
E

Lyo' \t \\ -- \i ll
?
,"t+ ! z.-
r
u- t.rr\t* !
?= R
(-
e (-x)t
t , nde$* dJ
+ S= x'l+!
*1 trs
--1-i".i* ph ho#,. -.'1, intene.e-Pl5

u,l ?.t+ t
I
I
=) (
G F

I r-Y'
I

rl

t', ha ',n{ e Y?r a ?*: j qteq{* ,d*, abo'.*- {u"* o'ln r

uA * . Qtrt

+1.1e- arn lq lr.,

b
i -.. *- \+-,
-.Uraaw .; o+ +h. t ct 11
,C..(-- L"i
t-
i
a*"F
{L4 ,*-.rt
I
prl
Y
t
@ ?(=
A
Le,q)

1 I ,: .,
e (2 A)
a" *j
,t)
t
( o ?
4,
t qb{
ci

(e LI
d
*
7t
Y
,?
I l*
X sr
|,6 I I I
.{" I
?- J
q rr{)

,
 TT (*,t: \e' q p"i** +'
I
or1
6no'Ph k = LL* 3rc
I :.
r* Lrr* i* 7
I

1t; e

t=t
4a *ir' t \1 -

H=
#+Bx
rj

+ rt : xe+ 3K

-/ t3+3L*4:o
ntx*?a *h x p
* *ta+
? xLlt+4)-r(K*$j=e
? tlr+E) tx*f;=o
:_''\"
)1=-t o\? )c*t

€*.;

I
 e h"plen I, g
ii

@ s lope <rF \,"o

6
)"oan po lnli ,

\,t
-fo z dz-tru
xz* Lt

rvQh

= lffr X +C-
-"'''-"--I
- i nlerr c.P+ c: -i :'.i
L4 I
I
J {
I

i cl.r:p C :- -__1 |

@ f.1, -* o, # q li nr-
6ire
n **c t ci#; :;'$,rT

/+* 5loy4. *ad !

aini

(A-;,) ' rn (*-xr) t

i

i
 --.!

r3 -Ja ln Pra,b br-413*14, F) *"'A +^ litr.r- o*d ,1:

(l,f 'ffir*.1*l*y*,
'yrftrapre.e{- -+t1*.

(o,o) a-d (zrr)

t '-?,
III
( Ea- ?,) = Y*
tx=-*x,i ,e-xr-

+ (t -o) = -,n (z-e)

+ 2wns(
I
+ 'ft"1 z
I

J
(* sluva* "$ +ln*'- linE- i>
T
a-

(b) f
"- lnoneqses Ltr Z- ,"'';+,
t tne neqgA bA t ort'l&'

(t,t)

(-t,D anrd (2,A)

(U"- *'; =
?rn (na-,a)

+( ?-'r) ..: \.r1 Q+,

+ 3.rn =I
II
+Yn $nr*-
@S 5loye* 4 ri.,ne- i> * .

Q;TT I lne b; I
:

t.r.lrr \.h5 Ll
( *t'lt ivrrraease b& J uniF.
',eouge.$.
 l\-

Jn ?*ob lemS tt7-2.\ p

{
l"+ 'eae[
?o, t
rF # 7o
i n*5 ctnd

da*ero..n} n*- +)",r- *1" pa o$ +r^r- liv*- eon&i'*i *f _

}}.*a.r, .

G*opf, +r',* liHc- ,

@a ,z) ; E
f
3r1)
I

(3,,
(1tt1
x
i
t
t
t
[i
a

E
(t.- I f"n (x,-x,;
il
t,

t
t
f,
:
) v-z) =Yn (g -t)
+ 2 =-hn
i:
ti. ? Tn -_?
Arrrr,, > loya = - |
i

r
r
I (-z,g); [2,,)
I

I
:
i
:
t
I z,r)

(Hr- *, = ^"n tre- &)

=) [t-:) i m (Z t-2)
+ -z: 4^.nr
-? ^rn= - +
.&B I '1
E3€*
t
f,r
&
\
r-
t
=---L"":{J
@ l1,z); VS,z)
l

,)r.
X

(?n I, ) =,'. (r.r-r.,)

=5 (4-e) = >n ts-r)

? o: '"tg)
) rrr= O
An5', *'|op e- = o

@a ,o) ; t{,2 )
Y

te.,a)

I ) x
rl

(Ar-?,) =t* Lx"-x,)

=) (e- o; = \r^ tZ-€)

+-oP.:acn

I r"n J "$n, J]
:a

Ao$.. f ,qn da$"qdl

_/
 {s-32 a. qS-32:
T"?\ +-i^r- lins_ \rro-i e,#ai-g
Fuot larn5

4+"s- po in]- ? annd h*5 . sl.p- ..n , Io., ?ra.ble v45

A5*3O, -fiU -+n- poinf- chye- -fr** + {n4-

@"n ,S +ra linz, -&, prob Vvns gl__ gL,S.,i
En ,1u.a*i un # ++^* l;nr-,

P=CL L) ,, w= ?
tzr5)
LttL)

brt_)
7=rnx+4.
+ z=(sxt)+ e
+ tr-S= C
=) C=-L

( t- z,) = rn (r- *,)

( -2) B t*- r)
t
II
!
) W,)
i
;
'#rc=2-)
6 A-2 r 3
A
l-

ir
)r
!
l-t) ? ?=att'
?*5 ( a,s)

tss- , j'rr

-
@
E
p=(r,3); -', =d
*

i
Y ,

;[ =
rnrr+ C (r, 1)
,i

=) s;=t,?.rr)+(. "X

+
6)

c.= 3+ t

t$*t
(
!7
= -e-

, 9,\

(X-U = tTr (rt-',)

'l

-) (?-3) = - (r- D
:)

;'$ E=e I
,
D

\-
(t-g)=-3 (6-r)
x n
-!
++
? I- a

=) l= 3-t
I

t_ t*L (,4, ,J

t4
 I

@, ?= e,-r); m=o I
YI I

I
I
I

Yrrt4*q I 1

ft=
J

'1- I
-
+ I
f i
I

) -\=(o x 2) +< /
I
I

(or-\)
+ C=-1 I

i
i

8- ?r) = .'.,C1"- !.,

=) Q(r,-z)
Q*O) =
=) @""';
1:

t
l.
4 'r t
i
Pv Gt,o) ;'lla',z. Y ldn$*"J I

(-t

(t- V)=wrfr-x')
+ C*-r)= tl,'r'(x+z)

+ .E 3 X4*
T
7 )t-* -L
,4"" .
 5lope{t poin*Ca,a)

ta- 4=ztt-r'T ?. I ll t
+ 3-3 = 2rc'l*t Hd- C,
6/ r F{
t

? {'2r*+} I

+ (a,
q
t i/
o?a rn
dr
Po
t,

t3-2) = ,,.-r3)
3
=) 3-2 = - q,*t 1 y=

:]o
* !t
3 A It
\ Bu*
'O
itoyz -t; r,,l (r,r;
C6- t) = -r (x-t)
t 7
* A-l = *x-+t
,to

'! o *,1 _L
) tc-x+$ d

]r-_--,_,,
 - End -.1-1"{-
en6t$rn-T. o+ +!* -'1\ ns L

@ I.-1,
L )(1-Xt
,r)
V l-o
-
2-o
=l 2-

({ -o)= + h-"J
+ lrt* I Xruq
L**J."--*
',

rtl 4
dZ- ,i r
I
t- aY)= I
(*rt l, t ?(z-f,r
X
2-l
2t t
(7-z) = tx'z )
+ f-,
*

) B4- L =1L-L
+3p 1c--z44,
+ 3t = )c+1
I

.tr
E t
if a= t* -E &
t
I
 I
\*fl = -f
Lt12)

c
fi =-)( ' *1t
,'- . \

L;> p+r,allal +"6

?=-=?L

(:-z>=- L (rc-r)
?-2 = -1c+1
=) a = - K{*e
$*
-,
-l

) eI A

-l-

L 3=- 't
L D pernl>"nJio'tlaYP ? = -t4

t?- ,.i I- ( x-+1)

.,.+ ;
=) A = z*L.,
M
:I

.-
 F
ztr -rs Fin do\n %ralion S- +d'* \tvrr- *r\$\ p'-oparzfitsS. S*
ff
iiit $praalt a'Qlt"'\t *t*t."t**f -ttr-*.,
6eolf}c,.l
$** o.,,
3r*
It
TE
5\ope- i wll*e.e-gt- uF.+u". a4r;oaHo"r d* a ti'.-(- e wrellyc\le{t.
ll
rli

Slope = Q; eo inl.^n- +r"r.- p"i+ (-zrS2

t:
ti
,il
'*i

$l (Z - il-- s Lx*)
=) E-3= ?x*L
+ ffi llr
;\
tr{tT;
@#
e.

@ btaye- =; ; con{ai"-iK r"i"+ k r)

,]

(a-1)=+tx-3)
+ i-r = *"-1
r.r-
d - zx*
L
Fi
=) II

+ {l ' 1"- | ifu..1'.

@) ConJ"in;nX- -l-r^z- prin$ (- e,t) on^ d (q ,;)

(a -5) = *.t t,t-t;
\, tJ
- dz- dt
xz-xl
-t t
att- +5
4 EJ Bf
$-1
\ fit
€{ s} *{-';

I
?ft= 5*+ r1,

5 * a= +*+S I

d*t
t
 Slopa= - 3 ; *$.
A-in*ert""P{-

i} =*lc*-C
? I-:-$rc+$ 4r"6

x- irt*en*cp+ = -ft i ?*in*errep+ * ot

.L paie& e&€ (-tro) o*,.d-to,t)

{.n
-rr,
= ':Y = -l--
1-I
I
0+{,

(.8*D) = r{x+*}
? $: kadf

e
,4*n* l

5 hpa und.$rn*d ; eo",-loin iq { r^.e- po in}" (s, r)

't *,S
Jt
ff_t
e Vn+'*o I ; con*q in i
rc +)d- pei.nl (*,, , -FJ

T=tt' A
Fftr$
&*j\4*rnr.B

k +af ; s,*nfuir. i \ \6+$

4r"- .p*ioT (-3r$ \4*
"ieott !x €T- e
d'
M
t
 Pernallel -L +t^,e-- linx.,
E= lx.) csrrfoini% _+*
'
*ain{. Grre)
-rn
= 2-

ta-t; = zt?t+,
+ ? = tr**.{A
6 ' zr*t A

@ P, raq ll" I J. ++tr linr t-2tr ,=-5 ; e{.r}+a;oi*t -}ru-

laioI {oro;

?=-5
+2
.\+ !.r- I
d -
= fC.*',$

?Lt *

tr t
2_

f"J . Ir L -,{
'
id'g
-O) = [ a-:
)

J
-?
t= z x*
1,*:

,l
 ^rn=C7

("a-z) =ox(t-*J
=) ?=2
M
{b %rg.r,Jie,rla.,a +" +}.s- line pu',,.+{r,-z)
nr*.t-*-,t.,cen$c.,*i^6.+1".{*
rn: - I
lff +"), = -z (x - r)
'= :2rc*2
+ X| 2
v
tu
".\
O ?u*y"oJ;o*ci*rt {, *r"* tinx- ? -L"t = - $; eon**ln i *6 +t"a poi nf
r t
Co,t ) .
4

LX
*'t) = -2tx-")
? ={**1,
,fo

I} _= _._ _=__J
 ?e'rp.ndl",J.,"5 i. {t^s- li"rr ?=t;.on*oi",k .T
i-
i"€'

poin* (O,E).
ft_il =1n (x-t)
-(= B
,*v,
=s(N-t) = 'vor)
+
>,lt =s

a
73-lz Find. +k- 5 lopu a,nd.
4-',ntco""+l
* ra.l. lir^e.

2= 2xt B ?+z ? =\
*, t". a n
+zx =' t*x*
P3 =)? '- z- -:! 4

?- itl-.oc.epl = 3 +? = --11( .+ .i

slop( = - L
fr s;
$'u-6=z
A -i.*en*S+ = |
.,il

) !: -!x +r
3l<*"4 =&
*[o F q,=-! e I i

+ ,7= -3rc*(
E/

6- tn+ene?* :2 i

I
I =') I. -3-"r*-*3
@ != ?-x+t
= _L
I

"tr.
I

*l"p e- = 2*
t
.tr- ; n{ eh ea-D 'l-=&
i n+avacap* I

1- = Tt*

i'.
 I
I

-.. i

&*L
-t_ 1(- L
(- + i'.

ilop e. = L
al*? I

.3", i"*<-na-e p* L
1- tn*qneep* Nur.,.-

t
€,) 3"-'* 24
ilv
t

,> ,3 * 3rc
t tl
c
-,
*--\-

1
? ?-'-

s I+ P €--
7= L L
H in-lene€ {
:1-o
5lope.= .,\*radu$ir."-.d,
t
p
v I

fr =
in*q., e*p* : No nA_
i

r3 -*" * &'*tph *?.e. !f *.,6- *E*eL i

,

-=I -
I
 i
{(=q<
\:*rsC ii
a

*-4a =21
ud Cx- z1
7
* {---A I.-: I

-}'
Y
-11 S"d x* inteno* Pt.-
I

s* *- rF

'a.
fx -_,to
T
:)

+ "/
* 7_,
+ ')L :
J,
i ," ,-
'' :J
'it r9 I

*lr
trn. !

{- ;n-le ne*p F
se* '?L=e

\{*
(- * {'*

(o r*,4)

'',, l
I
I

F
 F "d *rr.q n*e., u*p-l= I
i err-
1*- ?*rph
Off' aclc-g ea t^alJ-r oh *t+r d
lbl ffb"C"
-'lt r- a1r*oy-h.n

{9 2t* 3tr"4
Y
_T; {.,'
nd rc- i nte-neag l
5<+ o
(or?)
2 )c:, ( (a,o;
-'> \s'r

(g,o) I

" I

Ib '{'*d in*e.e oepi*

I

tr"
s c_** x:'j fJ

36. (
+ ff=
2-
t
(or?

#*

J
::::+J
r

't : {* f-r
E\J

*L -g
'd t- infen ., pf,
1*
{:, -{

-Qt = QD
_lt
fts" - lS
Fii

li, t'o,* (*,?)

T6 'frn d .5t
A*;n*en+"c0{*
Fii vr,t
H
froto
*L# -lc:'.
0 I

F
tA *"**O t
E

*
II t
F
II
r i
?
*€
I
I

;i
t:
.i (0, *)

@r)

i
I

t
i

\\
 -?fi S*+- & = fY

-la f;^A rr* tn*E* s""Fh

Y
srz*
tr*"j

5x: 18 ta,9
t8
I a {s e
rl8
\J,rO x
B,o)
-7 fi^& in{q+**F**
A-
;. -.-' '
H=.* j

{*'?
au .*

(0, 6)

E1

.a
J=f,
 U *0'3x l- O'n4. I

? O,,*d= o.B.x--{-t.?-

*E{ nL+-S
I

*To
$ nd 4r.- u* tn {eon-n-p F

*e+* B-.* t 'i

I
g r9)
,j
(-u'o)
tu
E
)c-- -3 **-+
X
-).3q(= -l?- :-

* x.= *et
*')
t-
*I 4ru d *trtp. A* \rntqn *f {.=

."6*- ** ?€- : ti
qr)
d* +
(o,,

ss 3= + \€*)
i
t
i
F
JAS-Jof I B"u!q
I
 -1
Cnq teo l,'t
.*t*nda,"d **- # ,nL e':tfl I
f
(x- !r)t + }()" = t?L

IrF rz'aelit^5 ,1ft = L

1te+ r.
..€
I sE t

'i -T1,-
- s*qr,drltud S*ro *F a"yr €{tertffoy, ,p
S
+\ ejrae-le* *l nad iu4 1, ,^,i+h e nnd-* rr o# +prr"-
omi6i n fu, c) i;
a*&L

€G f\
I
-'$-6 Y1ryI
"{
t inat€*. rtz+
Et4-*r.+ b $q*c:
Wi

E -,4 (
", r) = C.,r ,'i[)
r}
\,7
\
F' * onlarz * CE,I) =th, 4
€'
re:riir"5 (g,-g;? + (t--l1a
=
,x
=dE
=!

(pr.)'+ (VzlL=6u

;) [ta;'+tt-*'. te
:1

2 Lx-t)L t- cil-tlt" ,
_&-,

Y
(r,t) Cel*en = fu,
t) ' t r,9
nqdl ,r* t (*t)L +( F?)t
x
: J l+t
fer*
--.lZ-

(x- t)" + tt n)" tlE)"

'
*;
*.h. { x
')'+ q-
q
t
r,

..r\
S.S-'
 !
i

ts ; (h,q:
t :-

i
i
Yb=t (2 >

i
I

-.,o=J
-l (f ,9
t

=
(o, o) l

i
**".*Jqrr'-J vrl'
!
i
:: ' : ; : ' '-

;-l=n deaad {.;* (x-z)" + ( 6+*)t' t"

*

I I
{
i

(x-o;L+ (t-")"= ) (rt-z)'+ t1+f)t= 1.6

I

3" I
t
i
t
1

rtl* tra
:7 I
t
I
I
i:1e}}f<.F*&
\j
lS* rn;
I
t
t

t
I
I
I
qr-z;L+t[+3)L=rA
I
I
I

th?.
I
!
=? I
I
I

=) rca* ?" -? = o
#1,.-!
v.q&,*---a,E

,n,

W tt=2 I (1,, r) : (o,e)

'f1
:lonJqmd *o 't:.f i ;
!
t i
i
t
(x=q"*Q-*;z=2L I
t

1
:

<) xa+ (1-r)t= t

ft€.
fl
!^g
mle* vaqj .$*;*,
t

ra+q+"F = t !

* ?e + tt_ ?,t,L + t*L = t

i
I
t
I
I

* ?a+ga-*?*",*t=o
i

? n.+r&t*tt "o
l

tfu,.
W
L

(D "o=7;(h,k) = (*s,-2) ffi *= L i t*^,ki= (c,- iaj

I

6*an d*r* d
e=kn-"Uu
'$**, I
i

i:
(x+s)L + (Ht*i*= F"
4
a

I
l
sl\r
tx*o;i* I ***;a ; f:ilf
I i J
i
i

l
t6e*)"*
iI
d"t?
+ Lxt sle*- I I
i
i
i
i
3
I

i!
.

I
l:
tt -=fotltn T
i
I ol *tD',GTfl'.
I i:ill,;:r=l i I
I
I
*A:IA"re€. I
i
i
i
(r+512*c s a

I
tr
:

.
,
t
,:

A*l.t H +t*q ?*& -

+ xL+ lor+s5 + *aL t
4*"
r
fi
*
I

? r'+ 'fi"+
qQ t*ai t7 *? a-t *t2*
\t
.Tt .A

f*,-

{&*'';
&-#
-"--"q*-

{
,9

i
i
t
?
:

I
:

:
i ** ;*..€

-f
@ ".Ll- [5-r,)z= 1

br)
@ esn*(o = fo, r-l
r
C raad lt*g = t-

O \n*eracepIs,,
ld',?*q s* x=a

rr2 + (-r). -l
-l
rij \1--l)z = t
A
-) At =l- r '> tr-r= tr
+ 'tt.o :) ?= ttt t=o oYt ?" L
Co, o) (o: o) a*d ..1o,r)

2 (x-3;z + 2A' = I
) trt-gl n A'= 1 I

(aro)
@ c"rr,l-e-ro'1 ( 3, o)

@ r"adiu4 = L
@ Jn*.n** p*s ;

4e* 3=o

e-?)'= I
+ (1{-, = t-e
., , )t= -5- O n ?r: 1*

(t,o) *^.,d (t,9

@)
 ^,tz+-{z+qx+2A - 20 =o

+ xz+ Z.x.t_ * z-' + ?t + 2,4, [ +,r. + ZO + t+l

) (rt+z)z + tE +rt = r$

' [q) ce- n *-eru tr L r-)

" 'lx

(D rrad ir^4 z s {-t Irl-r\

)#
(cl i*4e-n
I

es* *€*
(t set- ?(*"$

(x+*i"* {be*t"?S et + L$tlle=?$

I
? Lx+e1a"' *1 { ir.l;'
.J
:

+ x*-z=tJzt t1

- t &.: ,T.,q S"det

k r ffi 3
a\,
,/)
(o, - !* .fel

r[*
 "r2-+ff**Qa*Ery"1*c* :

+ ?a+?.x"8* + L*+-3*-, L,6,L+ ?e * l***t r*g

l

+ (t+elL1 (?*o)t = ?
+ ft+*)L+ (t*ol'*3L- Y

{*} mrr}e*= t C-t e.) al

i#) pedrur*s
! ll ' -

*e
v
(c.l n*en

"g* 1fl'' *
r*" "ga*

i:c.+g)2-+ t e) ;t + tt's)t.?
l
+ tq*z)z = 5 + 1*I -rjt i S
r-) ?(s -L*.ff
?; 2J iF-

kel{r'* I (o, 2t ry
W
['
I

,-I
+ rn-s + 2.*. t of t)* * tr+ ?,fr.{*{,{f tr
Er L
{.1
,

* {.,r++}*+ e ryr&} t* T
t!

t*: r*n€qv* x.(: i=, - Li

H ** *e*ik* = ,g
I H

Lq irt-i*"va**p*>:

5** ga{* x-r *

fi*"
r I!r e+-
{ x*-ie"}o * g \t L.
t
? ft;- *+& n}
*ft*
%n

l*& tg-
+ \lr* a) e
l
** t,
?;
? .F
tn
\ .e
{*

I'\\- i
 1
$n*" * rgr* !A. f"
4.

? 'q&
4* (t- tt*u
*) xL+ .d"- *.#." +-e-- ai e-6
=> rua + tT-*)*r-1
s) rc?- +* ("(*u)* * Ll Y

La) cenfu w r (o, u) br*

tbJ ruqJius= L
!

\3J rrl *a"a upfu:

*$* F{-+ t=O

l.i

r3* t *el
?g'. 1r

* ta-o + :_-.
rE
E :=
*

t
ps c ar?
{r ,o) t v H* 1
i
! t* s *) )
lu ,9

A
\
 ' d'l
a.1ye#en # 'e.e*&
*iaek_

Ca'rlzra (rra)
t
t-
e*T.s fWrrt segg
qs
+eg-*
pa'rn*- [-rrS !
:
) C!r, u) : ( l,o) j

* {xr?}* {-3,* :

t u- l-,it
t tr= - *-:L . r? L ,

* {x-'3t; tB**:t**'Y} tuq-- .

* {,* 3- ** + {*t* hL
* tJ +t= Ylz'
l

+ 'ftes *,fi

tx- i)t+ 1I* = ?&

rt
iF
It

l
!

T
 €9 Cnn*.r, C,g,,) a.nd 1*,n+* +- {q^*- ft-"rrn ir.

I
dI";*..
&"'fun G 3r,)
t
*l.}*ei q-
G1

G+ 3)"+ Q-r)' = ?

@;

l--
 g, W,*h .enolp.,n$-.
"$
q di***J**'(q,u)
a^*d (cnr)

( 4+a \ B+t
,4-rr'
\-E, T/
= (lrtJ : een*e'a

\a) e ^\
LI I i,. i.
J G - o) "+ ([*DL
*-
=..[ 4+ r
( rt- L)t + L"&-2jt = E
Qtut

[N_ -
 I
i 'i i i

Cnr*o- ('lr-z) -) ',

YT I
]

A,q can*en , tq,-z) -)-

t

=3
Y|qdi,^s .L ,v
tI

(x- qf + (q+*-;'= 32- I

I
i

r ii

) C"-") z+ t ?+t)t =7

@ (x+ r)' + ct-r)" ) = : I

eerr*"e-ra , tg, 3) v

Aw,(l)

x
c-un*uw: (P,-?)

tt

I
 Ch.gt e\>-Q"l

@ f"r,c*ion: F
li
h ing*f
o**ft'i- .
cqan?>p".ds +. ,,-<xcdl
t
t:+ i> ,bt &* ^n1rYx- -++"n 62rnA ak-*u.n*.-
F

t*.c- .d.,rrro,in +. e.oYtfaz9

, _l.o +hr--
Poncr
"i't:l
r':1'
'

#la:r"u'-: a-l,a-rrne-1ft+- \11 ++.r- \--a6.tik"

*
.i Satq+f o n i-q Re lq*on : Rn- lo*tsn :
I I

+ I
+
i
fl trne tio n F^n"tlon No* q F..",e*ion
I
J.::*-..#-J
I

tI I
L Col
Al *l.q
,I
q M x
U*"4
*.ot =oxq I

FI o {x
r:h *" I 5 R,*IrLri l-r
'Uq
L "."_J
Glrf;"rr, i k

* Bo+h ''E ''e{io?1 a.wd R.ta#on lr,.* da rnq irr

a*d Rar ?e_
\
!t

o F.^q**{on i} -fn{- st oF el
*
,i F-f.-.
-l'
I :Y1 pr+* S
"P

n
@ R*',q" tr i.\ $u*o*.lon !:
""\"*t,
- '="t-: l\
l$- -
 { -l n}
Ex o*npka-l Lj#
r-.
De'^^ln I
{'.
ri M, g, k} Ra%:,.{ 6o8, ody, ,r* -:f

,- i"'
l-
X

I-prici* Fo**, #x lici* Foorn

3x+
?* S 3=&*)= - 3,r#S
t ?- ..t
o -13
A.{c*) = r*-z- 6

-Th4 diffi-",ur,"c.
i-

f,*"tfro {-oln
aLtro Ii**F "{ r

{c*+^1 - {,g
I

h
\*o I

Y
.R It+h) )adh ,+ &w,
4c*s fco*; -
S+") -x
{ru+r) - f-crnl
1( ?t++a x t
r1
l+h+l

lr---
FF<r^,c-is€:
+

I.t i*sol 5de*q Jt*

*T}lzn
doyn*1"., . oqd ha
Y
Js+"ra"r,, irl,. wh e*l,*:n €qtl,h naale+tnn,'hapn esn;,'4t
* -t-..d'err,

@ { tr,g), $a,e ),Q,e) (e.,,o}}

+ :?'No* a d.notibr, ,
!+

Do* -)

R*y.,t4 rt( ) o)
M
(0,-r; , Cr,g),("? &),lg,F)
{ )

+ F.^ne*, or.t

a
{ a t'l,r,tT
L*ff {-2.,8,}}
&*,

+ No I {& {*r, o{on

O\nnq iy1 '
{-t,-s,-2,-q
R"^Xar
{'0, t,L,s)L+ t

",4f, <l
@ { tr, r&), tr,€), (c 3)c , l
$

Po.*.1 + -2.,-t, o,tt

R"^f {a )
t-

3l-42- Da*ura-ning wi^-*Lora -{+s eao'**ror" &fl*s t

a t *o*ion # ,. ^

o t{
d
,L
:i
@ u=t{l -tr €9 r*yt= !

l- t^n*dovr Itat * {**$;orn. i

I

) t =t'[ t-x
fg 6"2r3-3Lr-i l@ At t-rcL
= I
I
t
!

I
I &o* +. no*f oyl
F*."*{ot1 ,
? A=tJt-r" I

L
I

3x-
I
i

N"{' ,r {-*}lor. t,
ii
Y: |

(
!:

3= lxl
i1
?er- r-

Fr^rn.t*f 'sm ffi *={ +

I
9
!*
tut"ur S{"'y-3
-

x:t.l{ i. .'\ nr-

ui:r
= -ri
,\
i- i{.
J

r
€, _,!

d- V
^.-

h*no$" n
}{a* a &",.'li ua +t = )t-3
.!-

F."t c*ion

I
 rL 4{ r
t+3trt',
€* t

+ rd" = tt- + 3tt= ,1- ?-1u

+ a"=
xz-
Ll
I
Lt {-
fi 3:s
t*? x3
t= t \ *4_
:) f t':f */
.-h.
-t t

-5

s."rr*&1" F1 . . lIe* { $,.*"+ *a

r
435A Find +h{- -[rr * €** i* {.^tq#en.
.\

qet $(o). (tl ${r> t"r -€c,) U $t-$ t1$t9

4.*i= 3rz* 2x - t

$ur a+2*t t

+f* 3 - L- 1 A
c1
:
A:
Jt\\i/ 0*.o \
I
3*- tx- - .-*

) Srt}++r.- t) = - lrtl -
"r,*C1
-[ou+*1'= " g (rr,z+ 2 .)e, t* , + ?r*Z *1
3rt2+ 6r- * $$21 - z-
= 3rtl ,1.3x-+-i
 =

4 tz*1 = ?. (2t)L * ?.;2r< -t l

B, {rL -i- tx -4 = tLrtt *z111*- t

r(r+5) = e Cz-+t ):"* ,, tx,*u'') - t

at
= 3 C:ra+ z?d{.t^t) + Lre+1h -

= ?x-z * 6x-h + ?hL {- 2-x-tr'-2h -'t

(+,-:)

/' r rtlt
<*) ' 74\
_[t")= _!
$ (t): o
+ t*'). = O

X3* t

- x*-rt {

(rtzrr) xt+! o
)c+t
".-_+/t
t)t-l r*-z+ e.r-+t'- H 2L
* tx*; R+
( tr+t) +\ .)t+s
La+
T:FS ]*-

-f (q*l = (t")Lt
q'(z-t
tx*{ ?-n*t

-4 tx*r,,) &r") L4 ra+ Lrh *hl _l

L*+'n) + t 1L+h +ct

n
A"a,

L
 \

Cr+'+ ao-

$to; = o \* +tx*

{('l = 'lz * (rc+ r"; = k+trll + 1+{1

{t-r) = o
aL+ l*h *-ui *a{ h
ferrt = {-t'I-
*{qp1 :- ta-J r
&*,; : ( xfl )a + Lx+i,r

x"J ?r+ I'l rt+ I

A*,
12* 3.+ 2

:1
*tv;= I- 1-
t
L
*-:
- (t+q\ t- *tQ = ''
1(ltl?)
&
-e
tI .!.

{to) = t -* I
I
(ri+I)z
I t -ft

{cs)= r- |)1 =-8 f\

., I
*(x+ =I-
.F
.'#*-
1n1
rltr.l-vt+*}}

+ t-rc)= t- {
(*x+U z'
&"*'
- -f C*> :. J t:t -+
[rsl]r-
-ttt+r) =I- L

,, {t<**:z

I
€} {"r = aL+2-

Do**ir,: Atl n.\ .yrr,r-nqVurrs/ {"em-}

n .nZ
* }.
..@ Jtx):
12+!
t--.\
I )o **;* , /l-ti n*t rl. r.,bcrry / tr€ni
'x
i4 ff*: rt2- r.6

Itrlft,r-Ln'
{ X€R.i k{\,7+-i
1
' + ':..,. I

64 i"J{
x+1 lt5-lx---
161911, o
:'q x3-t x- ')t( rc'l{L} Cx- 2; = a;

.' . pojx* -2 ) x,7

D"**; {,*" fR : zf-1 trl iLo t xy'rT

i-* c).)
VE
1- 1C F

ft
,t
(
D- Taarh I x-€R I rs x}
.l
\x*)
-
D*n*in1
{ren: ">?}
i _L
'f,

@ {<,;
*E* L
1,,
D"rrsi t{
a\ K8R: l
6* hr=)
--
u+3
. i
l

=-L

D" t7\lu.a-lll 'I

{ Ke (: .:r
}-?, r.fia}

{F-"{ E* *t*- "*rma $ ***, "!

t; !
*'htr'.&

*t+-s-- Srio*t*t Ew p"*-i: ("):(d) , ql* n

I

:. .
' --: .

toJ'+h-- ,Ju*;o.
-\

ki S lo": LI) S-6) i4)

(s: tF ,ft).tte;.

(r) St) cs1 Sr S-A) (tj LA r$.q)'tq (h)

dr*

P"
 @ $^r= 3rc+t ; As)='Q'.-3

$*? Cx) = 3rc-rt+2x-$'= Srr+t

Do'noi^,{*"K}

€-a) (x; = 3*+ r -Zr*B r+F

Do'nain:
{x e n j
S,6)tn; = G.+r), (2x-3)
6rtz - )x + rL - l2- = 6*_x_r2-

Dnn* i", '" {.*R}

t'-i
{ 3"+t
( 4d ) r''.) : Zrt- S

Do-o I
{rceR'. 'K t&\
s"7 i t/
AIG

F-A(4) z 4r++=Ir

({ .?) t rl ; 6>r a'- I -rz_ 2q-tt=lO

e (l1 i &xr +4
t r -3 -i
r
F

b
L
 €, {u = Qr.*J ]
Ec*) = {xs+t

$+6t (e = ?*'+3 + ir,-&+I, * {n3 + gr..+t

D*"in: { *€4
(-a: Lx) = {x"+g - 4r.o-1 = -4t'+2*+ 2 , :'

Duo,n*inr { " *4
d a,rcr; = (2r"*3) $x$+t)
8x5+2rtz + Jtr3 + 3 8*5 + 12*3*

Dr*o in: { te 4
2f+ 3 a1134.1s- Q
?
Q),", tttl+L I
.-+ **'* *
rI
=) ** tA- \3
t
t .

II
Do^oi",',
i K*k i z* (-+f l i
I

+ 2xG)z+t = 1.x a? + ax? +{t : 'l 30

:
C*A)(a): 1xt#

S.6) tn,, : 8xz$rlt.l (uf +tx-{?}a*}" 3Cg

2xt1+? 3.+B 6
tr: : 4x f+t
-;."*.r-#-
=
-*,@,
q+ t
E

&*=,
 :
fru = ra i {G)=x

$ *?) (x) \t t +.'rt-

. I 'f
.-. I i-
rl ei

porno i",1
{ X- € H1 I

$-altrr; = ln.i-rr )

f"* ii
{ r*x1
,\11

$,?) cr) = lxl ,x -|

Do''.oinl {r.ee}

Q: ru -
L

x
D, i; I { rteq ,, 'tL +a i
)

d"a )q.a)= lsl+g ={

S-7; tt> = ttt-',
-n
t'3) : IQI,P'='q
*'
(r) llt
\H ) - I
I
J
:l
ilw'
1

t-
@:F,*p x-r ;

Do** in'. { x-eR : r< } I r rc S t}

{*+R. I 1 <rt < q}
--)

S-$ t": = rr- I t-x

Do*.;n: { z€ tR. : I -( x."}
d'X)ot = ({=--il. 1.1r

Dornairn,, { t+n I t f x <t}

l|-

(.1 x- t
$r'v :i.

Do*.*inr{*e X,Isx*u} #i
$nt:t*; = *-r +-

€-? k) 4" q

($ 'Ai (a) I'ee

l' ,_
{
\fr )rr: : {-f"r
*d#.#

tu
=

J?-l
 g {.,.,, =ffi ; ftcx>=Ifz , j. :1 I
1' 11 I ,
r.j
$n?l(n)=.lr(+r+-fr
Do"'rin I { x-€ R, ,, K=--r . qnd
x,*o 1
t,
I
)

I
j
d-4."1 fk*-t \a
-=
{

Do**t"l I {rr€*.: x}-tawnd

rc* {
€,7).q = @) (g) qE
. 'rx

Dor"* i",: a"

1tgR,: ,.ir o^d z*a
)

tfl.u =
.la#{
{
T
,c.{E-
L
a
Do-oir..i {t€rK: t! +
-n
8Y)(s)=.tr-r +*d nT+t=r*t =1
=

l+-?) (1) Jt+r -t= €-+

(*.7) tn: = ({z+r-).| Jg
=

t#, .): r {r"[

a,
JT
t
#- E

b
@ (i*.', -S*r= Sre-.i*-t a,ndft:rk)= [-t*,
S*t i-h. {."o{{on ry'

=) *"1 = 3rt +-l

kt*) = z
I
ff+6)t)r) 6 fx
3rt+'t +7 = ( - d*
+ 6-t-3x-r
r+i

s- -z
Tx

{td
r-t-??$
,i3* Y*

@ {") =lu-*a
t"*) tg - 4(iiii+g *(q ,x-l ?
h
{, + 4r, +$-*d .g
t

tu
€, {*1 = 3rz+ L
{c**1 - d*l g G+ r.,;.+ z (
h

3 !x1+2rch+h?':/- 3ra -E

3"#+ 2x1", * hL - Z4
b
lr
i
( r *+ h)
s 2x+h
il
6, {tq = $r,-r- }u*(
fc.u12 -{c9 g ftL+ ry}- z(x+fi) +6 - (3ro'-2"+d)
h-
g t't'+ 2 xt'* h9 - 2h +€*s*lW_k

,p,/-,{r-h +gh"* 2h - Bxt'

L,

V((x-+au-z)
,r:

(xa sL*-Z
L)
'tr"
l-
{' (x )
r+$

{c** x; -Sr"l qt+h* 3 -r+"3

h
.#*-ff'* h
(t+t+ 3J (x*3;
l,i
I
.l.

""k' t
('x+l+r) t)."l SJ .I<

Cx+4r*,*) tK**) #*:.1.-.

 I
i

'a) $u S"7a

:'.-1
sq:?
{r*u) -{,ry Cx+u)*cr ' tr*t
h
i

5r+- Sh Slt
e+h -t r ry-
,L
d+
I

l.\

(x+) (5r+sh) - sxlx+l"- a)

(tr+r.-.r) C}c-u)

h
,#+ tr-:
:lri.l> !
-*d+ gx
Cfe+lt- q )(x"" c,)

- 4by t
C )*1. - q){}, q)
7
a
i

-qo
Cx{'t - q) (L- dr)

': l' ,#*.^ )

ry.*h

..
 t--
{"} '.tz+t

(^t n
* Cr+ r) -*t*; .ffi;il &$ r-
.i. I
i1

$r*r^+r - Jru+ t
x
$["lt* +""ffir
r a qfiii-
1
t.- .{-x;r,l
i'!

.; r:** \ ' L -, F+:

i '-l1Kr h+l ) t.l)tlr )-
-t-..rF"\
hUtJnrr *-llt*t./

.rG++ il-- 1

h($ffi+Jru')

U'(lr.--ri + iEl )
i
i

e
t t"l uq ! "l .ir't 1

\, /t

! i s----rJ!*,
al
\ 6,,n, s r") = x2 - 7*-* 3, -$*a +te- .ral*r1s,l S'' * suik-t"

{u+ -f.*1 * & !'

? tt- 3".+3 = 3t
t rt1- gx- - z.$ = o
+ ez- 7* +trr- - 2$ = o

=) a(r.r-Y) *al tr-?)=o

+ (z-?) ( x+ et): o
1(-);O oYt t+t-*o
.f. .', lt= 7 o?, r.= -t1
* ')^-
F {^
--H*'

T$ &*> = 2x3+ A*q 7x -$ m*d {tU =5, r.rh,.t il +h&-

VA\, .e-
"$ A ?
+ {r2 - 5
{(u) = 2x 23 + Axz"
E fC + 4A+ l/1-5
QS+EA
=
{5+ttt= 5
+ tA= i $O
* A =-5
L
€* # {o;
I'lrcs; tI ff-]t t^
w qvud * (-g)= A , ,+ L# 'j +t-e
valoe # A?

txGa)*q
$(- a) =
*6*rl
oh

B * l*t ffili*
4-
4A tt
d

rh
Iii I : t ,*,.

-3-A t

=) -rz*ft:*g-?.A
SeE 6

A:-t
. r-)
l"'Je. 1]
\.'
!.,!
 Ci",4f'lavz Q.,Z

)r Va*14"o1 - li're 1u*1, :.: :., . ;-..

trl t
I
Y
I
Y
I I
t
I
I
I I
f I
I t
,i:1
I i

I
I
i
x t' ',' 'x
.*'l:
I
i
i
t t t I
t
t
I I
I
I

I
!

s11 i
i
Fl,'rc*i'on v lla* q > Nad- or

\*

t..
 er>c.i5q_.
!

6lu*r-, ?*fn ,$
Uga +r.q {-jnn- {**#o* =I
+. a^neway? po*fu (*f tn)
Y
.:.
2rA)
tq, l)
G (rl,l
(loro
.{;2) T x
!
(-+3) i
?
'!-

6,t F;"d Stuy o^nd {G,>.

te) Tr &S) posi*i,*. oy! n*3nd" tl

(d) d $C .r) pas'.ii,,q olD neprr*ive :

€) E** nh.f ua\u*5 "f * i: $,*3= o p

(fl) For. ,., hq* va\,*es ol * i : $r*: )* l

tA wtn+ ,i ln*- d.",**, -$ {:
Lt ) u hal F +\L vtarrtL -$ -f :
ti ) W h+ a*-s{-, *u.< t - \,,n1an csph l
Q'.t Whe+ i; {-}^j. int<.n rsg+
tr_ ?

tk) !{o r,, **.o daes +ir- !tr*- f"l r'n*"yng.**t +I*- qnrpi. i
(') Huw "f,t*r.l dsa* -l1"** lirnC- t-=S i"'lenx.f -{tq- toqpt, ?

t"J *r, u[*-r{ val,*el ut x &"s {ixJ =33

tf,l Rn * ket*- val,*r, o{ L Aoz-r {tx ) ' -2-?
L --s".A!
.4*
|a $to; =g i +(-t):-$
@ $(e)=o ; {(rr): t
I

?"si *-r v C

e hky*ive-
-:\ !

-3, I qnd [o

0 -i <lc< 6, e.d ro5"x < tt @

@ Dr^.qin,, { xeKi -6 (rt( tl1

O R*n", {r.eK., -$< *-.E}

G (:3,0 ) , 6 , n) a^*d (ta, o) -? r 6 o f o

(O ft,*) #
@ 3 $rns-s
O on.e- / L -*rrru. .

A0, 1

''}J* b )
/'\F

B
 . -.\

A**.109 -lr^o- +tq- e

I
I
I t,
van -furnctr sn,
1.*.s{i"w "nto,**

{^l = -3*t srt

(*l J: +\r. gai.ll q-r,z) *xr- ph "+ S :

r,-1
qnn

\"r
r I-r
ts x=-2,wha* iS *tx; f1

? kI*+ p" i'r* r5 0R

nlj I c1
: '.. -*- \
"U,e- yh cf.t,l

6na
Q) $ $c*l i-z ,\nh,+ i5 xl !L+ p"intrl ..ayr.c ofi . \:
-1*4
(*pu "F -l :
*\ :.
ttl W h*+ ir *t - do"r.,qir, d! f3
(.; L ir* +L" x-ir,-l:araepp}1, i{ \
"*16"
)

G.t L;s+ *xo- nracap!, rF l\er.o r"! u €,

1- '"+

"| +u* fis=rh "$S.

F-- .--i4r--rlt
 v
/irv

-},t-r)z+ t'(-r) a -3-5'€

G r,-8)

, ni1.
\
A-,

C - s; c-z)l + s.(-z)
-f k2-)=-2-2- ; G2)-22)

O , - gx"'* 5x '':'- 2 i'

+ 3x":5^'t*2=c
+ 3r^ - (x-+ x -2 :(r a,i

+ 3r-(x- 2)-t r (r-t;=a3

-*rZ syr I*- +- .!.

&

f.. - ;!

x 2L + sxL]= -t2+to: -l-

( t)
b, z)
[-s
*"d 1t f
1
t

.J

[- ax t -3)'* sx G s)] = -!3, -,- s

3 - -z-
tc\

1
(- T ,-z)
1r:
'

G} .4 tt '.au*-t ?!q'rn"Lerx , / <Kary

* Sn,tt +5p.6
) S?re- 5x :o
*l
+ xl*r- S) = o t=0 qi^d X:-L
3
L3"' )

o@;
 {,.r=#
-{ot
G +.*- 7o
in* (p, r+) 6?r} +hs.-
(*ft 'tl {t
(b-) :# z =t -1
v+}.a* !5 {*? urt"+ poin* ,> .*'*t^q
f' n^
o-r
6waph t(

Lc> $ {,*1 = ?, *!o+ i5 x? Nk-+ Toin{,si

q lre- ellli

-lte-
6**fr #$l n

(J,t W h* u -l-r^e- ;u'-.sr ir.r ++:

\ r,
t*l
" i$ **k,
L r.:-
) {i'.*,(- ?L- i,r*e.racep*F
t

UJ

a**
H!*
{
*$$;
e L;s1- +h€-
*
* i n*a"n"*fJ: i+
f*
ii"u nu"- ry c t'.,,€*.

d: +!q- "s+
Q'u*Pt'

A*
.+F
-:f'- (=

4+- -,,
{} d-- 6
4*r
r _lC -?

{rE) = -i
t3 t-J )
 o a-L
) t+e : 2x-lL
=) ?iit : (tt,e;

@ Do--- rri
{ f,e R,, ?r* 6J

-r<-\
e) ?-,,l€-
1r- c' f*.i ?-"]
=} 'E $=,i .. qr

* )c=*?-
@^

r.: { .:*"r
-1"=

An* l<_'{
2

.le}
/

n
f'&'

b-
 {.x
@ {,": 1t* t-

sl Ts -lro- po /L 2\ ov' +-:-

\a ?/
a
i n-t-
Q*:rb
,$+ ?
(U lS x.= t, wh** &*; hlks+ pm ir"r* ,': * o
+J*A- *
{}?'
B*Ph
q cqf-'
( J* g*= t , w}.q*
!
I
5 1 ? !* )'o+ p*;rr*ts; qrx*
eh +t4_
t*"p1" +
{-
?/ I

tJ) wrro+ ,i !,s_ &rn^in

"t {
-{ 1

,r
\e) L I rt* ++*e- tc* f o*.a r? ec ,lf *9, l*
c) .l

\$: L', + { l^..* t- i oJ e ra.,u p i (-:

rL -i lrs i"s i5

I #: *uo- trt J+
3*o
!.
!
. ,1 !.-' ^r
{,;
Y/
J..
Er iL

2
:** lft 1
t- e ar
w ,s

:\ r-F*€Fqss--affi *.* -='-------r---r-::::*-i

 ,?) 2, 11

'"F
q-2

&q) ; (q,9
c.g
t

6 2x
?(*2 =

+ 2x= X-t

) t = -L (-r.,0
: r,:

A p*"*ain;
{t€R, **{
e ?-0

,) 2x: e
+ ?r: o
(m-j
/-.^
,ai
\
:t ,/

fi* ?

f7 tvIJ^u _t\
t aAJ+',
\
\v I
:

b-..
 ChaP{-a Q.s
-.
\ r' o|1
€ Fro'' -firnctt

(-,
PI *a rn -k inl*ad of 'x.
{_
$t*>= 4r*",

t' p"ro{ru11
^ I r -lg r'
Lrdd '

r 1

FI u-*q r|1 -}(

tr!
l;!r€r' I
I
,( i',i: ..1
Sd - *t iri:-i' J
q*

-Ft*)=-$t*;

.f \l
,I d ti q
O A {n,*-'i u1.1 t! Ev€:n li e,{ 06\\
{i 'T: fl )
1t
\t

i5 5;;rntrrz-*a i a {"?it h *€.S p€ e 1- { o *U".

'[revt
a 4-*tn'
q,) A S-" c$i J a ',$ *.", d O-r: I
1!
.I
ti
i

tn
l', t I s6*""r,^rr-$o;e r^r,*u *nspac{- +
1r. t*EP
-{*++-i--+
<tlT\ )( ':.

-l-t*- ov) rA n
-!

Tl "h"e- ptr .F .., ,, uau^ i; s4rr.t','t*n i c

Qvo.r

Y+ .+ l'{\ rre spec:*- -}r, --l Ls* rt - aro i ) *l* "lU* e1.*"r lio',r
t{I n
---tFH
l"-,> x \5 ro:*- €\ S-,^" o*lieyr .
 ) oc-al Mo"itn* a..*d Loo*\ t4ini m-e

j\
-) l),\a
-r.r
-varlu*- )> +k looo i rrr Lr-lrl .r*\,*-n- 6\? l.cql
\l2 A)< i

rn in i*.^.".* ,qlt -e a.nrd ,j- o * $sYi^g* tq* vea!u-€. ,

'!/ \
-r-r I
fura eN*"n le_r 1.
p Fin.-r'<- 2L
, w €- u"? -$ )"r*5 a locql
wtaSirnq c^'nd +I€-
:1 r loe* l r-ra.xi-.n*.'r, i5 z
"rqt,ra.-

it ,2)
[=t, )
(-..
II II
s

_n
a- -l+ tri
aqb )&ne in 1+,A- dowra ivr crF &* a*io y1

+ha- .r,on*n-
Z.-*$*r )
"S oh*tnte- d f -f,*- q &b
o
t5 Ju$?",rrd'

IT"F
ipl, fc: e+b
1

4le
b*q "
t-
l
 Fxerrc-ise-l

YfI

Ii

.L
tz, t a)

Gu P) ,?)

$,9 ,d (s,o)
X
i
i. l- F;+]
:

@t:{
:

i
r-hc t*? *.u< io*or-bvd\1 t?,-2)
:1
:1.

it

ir
*Ys
:i'
il

15 f ') +t^a iolrrlvq (g,-r ))

I'
ir
a
i: CD Jec'.a u,*t
F

B
3
R =) Na
F
r!
l
R

E
s
t
I
@ J: { rnayreq3 i t, +t& i',-len va I tr,.)? I

E
? r.lo
:i

A9 ioJ-
Af,
t
:.
I
.t

l'
Je.aeo,si
3 tj Ii +hr= \ n*uy' vq t (1, S) )

,
2 Yns,

@ L i:* +hs- in€m*^lG)= .,r ylo rc-h + i5 ina neasi

, (trU
 L il* \* in{e-rova[(s) ,o11 whi"h
e-rr€a rinl_ I

(- t o, - r) ; tz,o) ; (2, s)
: Js J+'.evau* io"ol ly,arxf
'r*, ^* 2_ T li 'dns''

v.r!.a* i5 ;l '
+ Yns 14 locq i5 l0
I ]"nxi,,,-r', ,

?F

-'! 9 -ti"c-ne- fl loc.,,t t'r,ax frr_vn

= a * *)
*)l

-) Ne:

L;r+ +hs- YltLYrn *S,} '*'t* v.h i.t^ f t"j loo".\

W h"l {:lYt <* +f".- I o"*
lrra'X i .",,^*r-, v.a I ue-1 .1
I

='iqe -L*"+;* I*9 :

]auol h.41r it*"r *.r*g *$ _? ,)
-Th"e-
locol hn'a".Ytwl{X*q.. cryr( (} lO t
:\a
-? 12 , 6' tO
@.\
g L t+ +\* rntrrnbe h6)
"t wh ioh -[ ]-.os 4, \eal
-nT i I r-ut^
"r "n w )^* t +\4- iooal Ynthr\rfr"raVn rrq\,^es
+ r'!
t--:
Q:.$ j -t s0,a

@;
E--
._--..=_j__:
 @ fi'u ++,'e. ^buol4o_ .rYtq}iroU,r.,
#f on
t-. o
rr Bl

) -fhA qo\-*-tz- yr a.x i."^.^-n *s { re7

^,b = rO

IF:
l''
@ FinJ +tu- [.*+<- '"nivr I r-. !..ff\ -{ t'o,{
FF,

E
^Leo "i *Y^r

)
E',

Ei Scs) I
,*

2S- 3Z -rlu naPh # +*- fi**d!* q rvet1

4 -

n
\)*e-+hs- ft*qFt" L $^dl
-t-vu<- ,r
lal -1. t, o. u p*: rt s r..
:+
\.1

(U: -Thj- J"w*i., and n^nfto

*Th"€- rl-
(u ) i*t*ro v. I I a !t wh lc h J us -1q6.-l,o''

\5 rnry.leaJ ir"=7. d.e\,)€.4gi.,.?

, o**#o*,
*\{

\J) \ha{i*rr J\s- {r.dur. ',J (y€h .+,C

oLnl \,,Rro .
 Y
i
t
{i;1}}
I
Lq,a)
tt;?)
i
I
ta 'o; (t, o_) X I
I

I
I

Gz,6); (o,*3); (z,e) \

1
# 'i) o",,'.*i n i (x(1 iqtt
ft.e t
{ f € rRrosysB},o€ fa, {
{u
\ /q-
In\
L:J Jne
I
n ?a-:r YA ayi {::,o) ,4.^ d ( r, '*)
4
Fe nn e*-ri .4
*11 (-.r.- z) r** d tc , ?)
{
S] Fouo
z---\r ,1
89i
I

:'i:. :

,
U,o) /

OD Ofncatvn'.
)
\ )(€ iP.1

-t)
T\anq e
\
Alr rt.qoI Ituwtberrl
ild.,
\ a\, -f
\!/ lrrCrt.oS,
T (a
"{)
)

@ N ai-iuun
 ,t
.,1
1l
I
!o, t) I

-T I
1rv
(. r,-t)
-t (r ,}
?1

GA,r); (o,t) (%,,

( n
GJ -\l) o.rroin'. J
\
X€8,'. -zr1^<nJ
R^*t-r" i
\
frC,E.', -\ < ?s I]
@ fr,"r1€a-sr "-T 611 I\- F ,ll
)
*n<-a:i, o'r^ ( v)
D
T ,

@ Er*,r

@ (-rr rr) (?rz)

(
-,t ,3

(9,a)
<-1,-1)
:

-.-4

ti)..,,oui',,,
Q { Xerf ,, -g1 x-I 3)
?**16*r t 6e 'r, -2 s ?

G, Qa ,'2) ,*ri
("rL)
Jr,o n ea! i
?
Du rr"rn^l I o.?- O \-1 (z , g)

O Ne i{+..r,

{
33- 34 th.L
ft*opr"
,T L.1 .... i i
I I t

(*rt'' +-o t*t

*Thz rr *",t Ir
(o I eW , , $ **r , .a| wl',1.h \
*L .rl
-l"q
I a\ lO+a
l I

ax iw11nn"', ' Wh*t-

Vn
+^+ jr.e! aXt!+1
f11n€*
,7r.r h yn val,*-e I
(u: ll"'e. \nu-rn bo-rrs, !+ "'t ., *L uh.etr, + koj q lc.*l
.rni ., i r^,-r-, . Wh-+ q rre {h-e- a*-l * I ini v,r..vnyn v* [*x5 ?

a a

ir, e)

-^ f-
-h-r"{.o.,,
,O -Th-a h^9 q [oe 1 -fnAxt ffLU*Wl o{* J

a* d +hL l;"_ I Ylt.A/{ I I

'52 :

- f\ '' '

O rF,u- {-r.*{"n h3, lo"o\ v. i nt r*r 4{. l_rL

a'-r
a""",d 41.r* lao-,al f1
^rna.,xirr1rr,-,: ax3r€_ J

lfr.z^,
*.>-F--Fl: v
|-

Y
z
,)
,x

r\.
-Tw_ -|.^n.-{{on h^s t*"r-rl-"f ^m.4tr I \^v'r-"{,-41*1

q-l er^^ d. +ntr-- +-"^ loc-'.\ rnna,.xi * i5 t

"r,.rr,

o+c ikr.E*_ Il^rr's h h"+'loco"4 I

i
I ya=+- .q.. *irrl*"r f
4

,,,+ * 7T arn dT -Tr\L [."ge| i! *o,%

':'i i: r,i_ ._
-lt*l
(Q-* t
\-//

$F **fi D*+.ra6 ing.- alqr*lni.*tl4 v.r he*r"otr-

aauV {.^*+, i; aveh, oJd oYa 6*'i.It^en

S.*1 = rrrca
G} hCr) = 3d*5:
::) -Pf.: 4 (-q3 :> Ir cr; 3 Gx)a+ s

=. * 3 *345

-
-
t-: ',- N e la }ts:";
1
l

."!
6,) c,o, t
ffi &*)',
n
-FGx) 2r--
= <+'zt-,qLri-
GtL) = l-x
*. &
?r."+ I

|t e-i*1^e-rz
I
I
{ rx")
I %q
!

fl-\
h CN;
x qH l-tx; 2x
t't !
xl* f

F L", ? +*}
ht *; "-t +J,'r-+-=<

\- rtt
*x,l'. i
2rt
x
xt* |
&e
r
-
fx !
t
,

Jd
-h t"r!
1

o old
F

q7 -frL n '4
L
fr,,Ji"
JOY?
X*y\ c't- r

?-tq
,Ra *r^o- ob*oL.+e- rrn4x lr.'n o,o& +!+"
^"n
qb orlu*n* wnivrirnr,^yrr , il +h" slis+-, -,k
3 Jr"d.ur.,

AtA vl
(
l*-i Yn4...X iorr.*rq y,a\u1.* d y? lo"^,1 v,r,'vr,'vn,ri1

valw-9

YI
@ +
I

I (r,r)
I
a)
I: f".':".
\:}: J
(s,t;
x

Abco l,ctc- 'Tt1-61X.'1\11 tn hl tr>=t

l\ yn r\l.l\ \n\Uvn
$ ct)= 1

I i
S *{.a t
Tng\XItrfliltrn "fr*)= g' ,', ,

t\ .yh i n^'yrtt,t y\
S (u), t

ih
 @ Y
,tt) \
(?+"J
t

1 (-+,1)
7 e\
z 2- (or ?r)
i I

I tLzl / 12g

Abro\**q 'rrt\Axi u\^n = No rr.s.- Ab*ol*{*. .r*o.iaimcrh &(t) =1

'n
: .r-ninirn,'yn r N ovtc-
* . ",2r ini snu hn {<o) =f
ir

-
Iacal ,x^xi YI'1 L^*"Iir : No.riA* I oca-,]i mn-ax i m. lr rn -tcr>= t
!\
t\ rfT1 t 11 r n^t{yfl
= N oyr<*
1t rnl\nrv\,Il-YY1 {-t" ):'t-

60
A

\ (1,
, e)

?!. (g,.0
--1*-*----- *-)
*t
{-'e 3 t5

,A rr*!*{ e- ?"?€\f ir.,, t".wr 6yLf*__

t{ wtinr'y.1u1 y*1 =
No"u<_

I
I
I
I
fi'ta>e I Yyttdrn : hlonrr_
F!
tl .,14 I y1\ \"nLLyn Nioru*

L*
 @ F;od +di- ave?a?-c- n"q.ja of cU-*r( #

(q F*." o +"" ?* tb) I"-.m t += 3

-F(e:- $r,1
t
I f ,or - $0,
1

a- t
b-q
&.)- {e; - [-zx aL + t) - (r*.)
L
2-o
- rf { + - L
-
(-zrQ)2 +!-(t )
L
-{l(
- 8+1 -t
'l

-4
1=-

("1 Fr"o, t+ 1'

-F ttl $t'1
1*t

I
! '-'v

r
F

: l0
 'T*S-- 73-2(.I-I
,J17) I'!r'-
inJ A qven^"(*.
+tIruP- qver, d t-r*{-,*- # ellvrn*yu
{
,+

(q) E * -s +o -L
J c.) - fr-r1
Gi;-.t-3)
4l Cz)3* r,(*i) +-l [er'- a.(-a)*-t
_z*3

[-t* q+il - [-px +r+r]

{
.&

(-$-t.o) : -3+T9 = l7

(l,t E,o* --t {.o l- ("1 -l-r--"r f {o g

{cr) - Fry f,*) S,,1

- L -.r. I & *l-

It-z+il - .I- r+e J.. t,

! lg3- zp s +.rl - [ r-e+!
*L ri
L

tp* - a+ rl
a* 2
*2
?e
4 .L-
F

= Lt_
I
 t

Exqrn i nat'on

-Ptr.7 = Src-2
(q) F'.d +\A atvehrc\?g ^*^+z "f d^--t*-
{*,. I +- 17
-3

Ql Fl"d +\s ^1p^q{.'or",

*u- c€(cudl:*
li',2- crr'*oinr^-x-' q rrfttl
) afmr'd
k I $t*.1)
&t, l!r

@ -F cr; - $t': [sra T- Lsxr -{

s-r L
lS-A t0
e
t
-t j

"+ -l-k- ,.*^nf lirnx- c.nJ,rinil-"

e -ThA .f*,,.L

( 1, Stu) = (r, a) a^d ( s,{t?, = G, lt) ,*/

(r'?)
r1 {t,:= & '"
1"3 YN (:ee) : \*,}, L?, ra)
\*'"' f(g)= ts
tt-b 5
-;
(?- *,)= - (1-,l",) ^rr1
a-e-

9-l
l'

+(?-a)r s(*-t)
=) ? = 9r.-S+?
+ ?= Sx-L
 O ft(q= taL

"fr e* -2 +ot,
(a) F ind *r.r- a\renrctr t?rq +e- eho
\,
"+ F

i"u> # +"I't* raca,4f rir*

.,r*o.,'"..,^x. Cz,
?Gr)) *rr*d C ?( *

n"s
T@ Lt-{- [/r-S - l -2
t{} -i

fr<*

O rt. *kp e "S {r* gee an* linr- *n*oJ o t

Y
t! Hg*s =

r x ll
(a- t ) =- Rn 'l
1

* (t- 2) = -r L*t'4 a
e^r'

'"1
fi
5 *x_-,t'tC

*
{,
.2
V4-t
 )
n fx) )ta- 1x
=

tq) J +-\* d\ryLftq?Q- *q*u of

F"
l/
tu?
=Bt- L J- 3.
LbJ J-'nd S'e"
11y4 J'.n
p +t4- 3u*,,*f li,.rt-*

Con+a ,'r, r?. (a, h(e) ) **d (4 , h ({r,

A* @- i t1i -ft*> =trE:Bjf

1-z L
:r- x
^<-) l,\,,\
=.\t?
\
C4)

O -Tt\( sbp,- +r* seea,** linz- cunlni,,Y

"*-
(2, (at*)) = G ro),
"^^
d 'k,l.rto)= (qrt) -i hr..=S

( A - 1,\-- ''''n (rt-tr)

+ C1-o) = qtr-z)
+t = zrx -B
@- )

l
 CJ.qp+e- t"

il
lrrlsl "#*k-

lB 5ku+er. r+,,,.
?*Fh # aaol. {..*bo* f-:e {o \qb" I
-{}'nec- poi',{;

Y
brnJ (:,q. 1;aer'tt€*

*{
t lr r) (rr t)

t9, o) -) x
1
I
1

e9 -F rn) =ro Y
'i 3.i1
E:ffi -l
-1
I

:(

@ +,"t={Ia. 5a.ona R*"* F.*Jinn

-Y:9 Jl*l -.,

'.1-{-t i I t I l>

@ {*-)=*& t
tzr?) C*e- Fo**io4
(t,r)
X
.{ 1
!
.i
,f)3 +
s
 +

Y Abaut*+. V"Lr r*
{iu = Ix t

t q)

@{ r); J
x_
Yt

r)
&"ip Yboea" I

l-l

Y
C."gt** F.r,olrq
@ t,.)
,3)
(-'*-----
't->r3) t3r?)
\
X
i

C,rb- 'R*** En*.*'0"1

qlT
@:t*r= Y

t---=__*
,F,

I
 lI

.}
f rt x<o
{ll

@ d $t.) {- il 'r=0 T
oft
Qt+ I rt x )o J
.. .,t.}

$u, @ $e ,1 O *qo) ;C $e)

&,. ti

@ $c'Lj=z 0 {*q'; ?ri+t

@#. xi x
=ZXZ H.
._ 1,/ \z
{-c
=
-La I

2x-1 il -t sx< z
$ fcxy =
ci'
xs-2 r'<x(3

"f,'..uJ 6 {to; O +(r) : 0 {c.> 0{ r=>

€*
O $cu = Lx-t ,C {-*, = ?x*Q
{( x): ?-r{
:?-Fl-t
t = 2,2-tt
= 2Xo*
(r
=Q
I

J: ,.'. i"= -.

Q +,.) = ,*-?-
= *z
: Qx'2
: ?$'
s; I ind l-{^ d, * i., "+ (!;ii: i i
{. oudon,

@ Lr"*u ^T r'q4-en oopil

|e; Q',aph -h^r--

t&l BnsuA ++'!-

3n* ph ) s n d +1".4.-
Ytretrvrqrc

(€)Js+ eo n$iru ou5 *n t! J o*- in ?

I 2rr- if rt *o
{t*; =
t It
i'$- ..rc=o
.,

Y
c..
-.J.,-a
,i
I

1 1z-r\)
(z*7
*."-*-+-+-- 1" I l #--->
T
.X
I ,l

A tt " ***1 be"*}

€: #
C*l*taiR ', 1ft c^-rn

(r, ,)
l\
i\.r l
{ te&-1 A"{*
G N C, D lr o.n*i rr u orr,! "*+ ? =O.
a
 rt+ 3

6e $,*: =
-2r-3 iS "rc- L *L

;.
lqt
i
Gr,r)

tLrt"
(o,-3)

-?*"* r!" 4rl Y'tg*,tl *,*t*n*

t-a,o; j f ?,o); ro,-B)
6,
* i$)
t\
0 {g€tR: $st} f+e* +h( a,,qPu":}
{brt-}\.n aaou&

2rt+S $ "$ sr. 'i.*

(x)
€p+ -
t).

*Sr i$ xlo

* vroair',
6 fx+rR, :-r>€3 6l
\]., (-?, r

+*{-- *?
i$ (. $ -u) ; ro,- 3) r
I
1r,-s)
I

P--6*' G {A**: f<s}

@ N o i D i, cra=I-, ,q,"
tr ,rr-*J a{* ?c =u,

L ---:-'-]*-:--
t

-Ih"_ n
(
Yb'q I
t
t
F1 dt. \eet* rr:isa- d4""-d
*Co"-Jtuo ,) 6lven. W*i+{- J.{r',,Sion

*", e.m *. i.r {*,*.u i'.

I t
I

t'
E------* lL,)
*z
G t'D
+
I
t-
x
L

n
1( rl - !, ! oc_(O
J tg 1t
t d
-L # ocrt < r

(ta*,Q-" ,)
-/

@ ,,,fi
)

-rrr? +e_
,/ Aa

=LL +- 2
2*0
171 = 6{
Tx+L + 4<'71 (o
*r

+*,>
;'f ,?t ) o'
@r
@1 Beo\
 i
t? - 2'5
I y-ltrl Tsoora

LA -?A V/ n# q +t*- -f,.r',.#. n vfh^st

Ttr'"
+"- ff=rt 'F tr =
,.a , t,**. ,! .

€, sri$t*.d += +t^L \eFt q ,^",\

t= (*,*)n
€e 5tifiad {- +-t"< ni2h+ 1 *ni t5

'( = \)t*'n)a

r"i{**d n 'q *"{5 '

@ 5 J* w

ttt=*

@ 3l*-t*-d t-e-f 4 u^i+:,

t-t = rf
 \

/r \
u?-
i.sfig a
ft"{}e* e& e\bo,-.{- x * erxr)
ii

fr= (xB)
I
lied
-/ d = - '{-t".a vra* 'fio ne-*ian
f, = l} *i.i
{ l^s

.rl &{ to*"a .aLo..** {t*- tr ^x

i)
!r*r' *tr-.e-
qroqpL S
t. {rrl u
H
t4-
(- knowrn , J!.*-
Alp",ph ,F +r*_ vu\* {o*.{irn
8'+ (',1)'*$
i: +ar *af le*-lian *tb<*** *r.r-
?- *rd.: 3=&x) .

i! q bo.*.** *Xr--
I
Tic*e ; Th,e-ne- \'''r(f
"au{\..d
e v1
t t
I

l*"* izoyr +"q lt 5+n ee h.o<L b q *.{.- + 1

1 ($F<*--' 5+rue.}.*!
ff.
* ] -r, r?
(
s =a3

Va va*'
%s4'r.*-., llr 3+", eo !.ad otr &.J.* "S *

?
1
Cal.lpne*ad
+ 3=tog
Tt= f
4
 n
la
I

ttlc) il' *-o- t-

-- .: \.
j,' ,-,
z-,1L*-l

+ Lt"t) E ,"L torr) X

D; {ten3
R I
16**, ?*-'i

t-?- t
QCrc)= T
tuFr *I
L,.t
fr t
\j
-

,ts_

+ (*, e"x 3

@ hrx;= ..,l
"+-r-

(*

I
 Y

€1 &*= (tt-t)3+2-
''.
{t- z)=,, -tf
.x

@ -!*=a= q'tr
Y
,7
tt= =[ =l*
?
=-
{i JT-
frrn)

f*ro)

& 4n:3:"*re
t
{iR
s**

L _-- @-_
 ff"t 3 ln +< I- f \rt
I

a +* alr+rl
it?*,) ; trr+rf
v
..t. t?<*) :-f;1"+11 i

6** ed Bee(

m
@
r

-&*r =rr*- ?*a

? = rtt+*Ltr l" -l
{;
"t *dfi" L}"+{ } x
 -f*" )a -3'f-ltx*t?*
tr
r-,j

1tz+ trt_* *t?*

!{

+ + = ?r?4?*,a-3- *-&L r*€

+ !?*!?-
Fl
-\
rf
?, ftt+*)t \s@,6E*>*
+in
d4i
:

rJ
-L
?
Gf
r. t x"+a) e & *

*/
r+
R*
LJ
{ a+a)
?-
=

? t (a** (*4 t-

+w

F
t"u#
T

Ch"plcra B,l
-Ir k-{nu rrrier- r,L*rs', & S t!o*,? }inean &***,ur",
19 incna4s ,-t : *e* *rqc.ti .t'
e*nr4* *t.
(ql {r*y = Er-?-

+ *lope- r $ ) vr.hie-1n i5 po* i&, v.c=,

lhe
A

-*t^.*oU; s \r
ti lRert?qsr}14.
t
on +Le-
i**er*vol t- o1l,
"u)
.-i
(b) ?c",1 = -Qrr#f,

+ *l*pc = -Z whie'ln $ *ff*i"<*.

1l',& &noq*ner, .{ rS de * re e.asi F!r
#1
{rc: in-} eG *se t t* €e , *S }.

q
 5 c(FP osa- -tru*

G So\oa {*r= o, io\.,e -t*> ) o - \

g t\"e- $rD=
?tu. O 3.1,,e- T, x) < .ftr") ,. l

CG* h rt)9 a
t
'l-
i:

= *^.'d
i

a ?t*) lqb*! +!q--,,po,nl-

h- r.
--rttztJ*
vaepna_So-,*s
+1,* so l.**ru rt Jo *iq aq*o,{o.ri
n
rTv.x);
tr*), , *

(kli
j'E . -lx- t }ci
{ \ s

fs ta- r-o
1

+ ryr ) T

+ 1x =.1 -\ri
-)
/
r
t-' /
) 4
,+
I
-\ .i
I I

i
I

{tx;
:

w)
,1'.i sffg
?-( {rc'l - 2x l5
) S
-/ 'f }(* *\ (xS
-/ -C

6"r. =6
+ 1s1
x*L =

G) 1J
{ &r "-+
./ :4r x !;, I
( I

3)' t

X ( t;
?= -2x-+s

L
 @ su*" *l €4f
/t-\ x)-- - 2z+ 15
\
@ 5oh- {*r-o,, O 5o \vq {r> <o
L
O Sotuq -R*r= 3alua { rt)
ff,,r) flO?
o Q,qrL ,a*-4\19
11d ldA
'ri
^."J frrff*)
\
\t r..
+r"*,

p" ini= {h*"i- \zepn<-eox* +],u,. s.l.cJion {" .+rn**

a1v*{, or^, {r,
tu = (.',")

@ &r*5<o,r.:
3lc+- S' e {>
: .rrdl
> n.lrr
-5
\4r'lE *

-2 ')t:. -
-
*c,
I
e
) x<-q{
,1

&r; > ff}]

3x-+-5 = -L:l.+l5
,s 1(- -- I C) * ?> Z
-\
7-)(=L

(:,'j
.t ->

T=
U
-Lxt" F5

ut
fi

- ri
I -X

. . (rr,!
! A'?tr' I

I
 Y ,'1 _F:
-ll

trs*l
ae,sz)
-a
GauT
Gze,"i
/(

(*l Solr* {"t= BL , (b) S,,lue- S*1= 5}.

{a} 5* trve- S,4 * *' , Si fu l"e- n

+crcl) gZ.
(* *t,a_ $- x) s 52.
t$: Solve- ,:i ( +fttx) <52 .

A*
3=
s2 ; 1= ?* 9 i uri

fr= 5L i 1c: eg ', ;.

i/" :

E=? _r
r, -.
X*- -
ndl
AE !

@ >32 )

@ Hrssz i rrS6B
I a < sz
\- .

)l'
'{. i ---.

-28{ rc<(3
 . ^l- Y
ert,q9 ?= a*")

(:, zo)
(r*rr:i
r
\

8i Soty4 .{O, 'tb) 9.}''e

t.*l ?.*t=(0.
fa) iol

te) 5o\, * ff*,)s60, 6l ,5a\,u o<fr,*l{(o.

,4*,
@ !p=."o ) .rt=5
e .-1
t!
ELJ
!i

,
t 3 -.15 '.

O H=o ) rt=15

*$* 0 ?O II ?(<5
@ -j *'+
i.

)
I

O o<
f,*l(6o -+5 <1
:.J : 1\
I
Y
I

3,fi4 \ ,l
(a;s)
tI
v
3= ?tx)

o\1 I &, ?r*)

lb) 5o \va- {\*- i'u-1uali\ I

M @ +i=:8 i ?'== .@ -8
".<
)
@
I

&=Tn)

[*,' 5o l,re- -lu. €"t(r.+tro!

lr
,,
C
*tt)=7tlt)
S) Sa'lve.- +L._
'in a1r,t-ct 1 i +y: {,.)<Q,x;
-s
t?l
l*-fi\
@ 'i= zj'1,.S @ t<z
 Y
,6)
'Ort?
f= tt;lrs

(+t,-*)
cc,r-g)
v ?<ry

C Selve- +i..* q),q*i..nr {?n:=

?tg
?tx)( {trrq
tbJ 5o\'uu +t'€- inaoL"o tCU
lf t :

/tt @ ^x-= -ti) ?=-8

-# <r <g
t.

Gt,7) T
,i) t * htx)

,}
l

t 3..")
:
(or-s) (T, 4) {
t

i
.+ ={rg
i

!
t*: 6., !t,a* "+J"* u*g-o*+ioy.,, -ffa,: tr{ ,r)
tb) 5o lv. -|u ,n a{r-,r? t; A(a)< {r"_, < h rg
?.;
& 1r:? [*-€.

L-,\ \}I
I
t
(x*(;
 . Tlu- css* C, irr d"\tarr!', S-."*ndo-f,*'o- vruar,,.t {Gr-*rt.

*k*,r&6-i5( i., e.: +"1-*

"{o*&o,* :=,-
r-.cx) O'25rc + el
0
=
t.
\rt l\*ff- t rj, -ld. eYz
nu_nrb
l
"f ,r1?\r.: d*lvan.

tel uth+ 's +ni- ",s{- # n

.l .
drrrvas z=*O
Pq
'"ilii ?

,4.a: :

jl t= q (ao)
8O 1
= o,zsl^ EO + q O
tJ.O
= *rr*'i {ic
=6os
I

(b S -{"r^^- o,r} # ,m*otf t.r^c vi

,? *ra"eJr".-
-s ."60$, l** **f, tr";t$ dU *u.*-
petaS&h
doi va*)

rfl
,/-.fris
Ccq =60 \ \
'
\
>!i
E

6 O :- q'2S x *{0
? 5*
t 3- 20
-\ t= €O ^rr*i lcs

L
 Yto rn r3€. *h.n *tso ' hhat r: +ha re'r#.,}f.! m+>r
brum Le=ra
"p *l[r-5 +],* S*-OgUrt Cqrn
i^
dta ira l

A-*
? +{rrc
\
=> 1L < terO .}?-,tr
1*"5.

Lt.l v.{h.t- i; -lr€- i hpl i4d &*qlo s f

An'
Qcxg = g,2.S%+4o

-l'I.€-- vallur _
"+ K eanrof ta \f-Q **r u e- ,

I
"e >*

olln{rq i
{rc€R: tt}a}
@ __pb* Cha,oqesr
*Thz-
-ncrrth 11 .os* C-, i', .lo\\o16<
n
-F
c
(J-'*"J &+4' -r.q o-*T-t o1n €\
I
_ ._ lr, i-li ,,1
F\snz- plo.., ;> bnod-\ J t* -i{".- Lr',*}to.,
r\
q-ex-)= o'z(x$ S, h|\g_Eq
\i: . -fl bse:t-rb*-ra .$ rainulr5
lt-s"A, "I '

[r\l Wha+ ] +nz_ ec+ ",{

a"
Lo +tt( ov\ +l^q- *,"
?}o",r^*
x= 50 rr''l i,"eu*eg ?

(o>+-= q.)
-&n 1' 'i\

i lf rc=Sg ,, C(so) : o ,?..6,X 50 +$

; l 26
W t>d +s
t_

3tS
=
,nf
(b) 6*puos*-- Ju+ ?nno"'tnk bill S *zl,C1 ,
ff-rt* l4,w
**-& \nnihlrl€! d', a tr* upe-- Jt*- phrr* ?
A
-*ffi-*i_ '.-Q't,24
:a+ $ = 2J.{$
) o'24 x-: ra,Ll
+ )c=41 .v^iru-t-{e5

I
I ^r;'*
}***?.,*:
L

I
i
-1
a,*.n.&&f ' ooffti€d
Jt-ti +h*+
i
:
i
f y,*s*- -&t"g-
S ,g-.d
*l+.€*
1t{.cin **f Jz-.,-or,&d p +n -I-sl"iqb o+,4
,

fon*e,.rat qft€- &llu*i Tk **^'r..{'4.g1

ft*u*n %
W\u rae- 17
Y
,> *lte_ p*?{
*'.
:; ,- !-

591
I

= - Q5o rr50p

Dtp) = \
*- .-:.
i..\

S) trnd -|q*- €11+ri;t.,ai,&yn

f'rai e.<-
r\
.*tB *+t*
*bs}"'
i**:

l{r*l
i

I
\
-/

i
+

t<

,11

TF

;i#

r
tb D&*mins- -{+'L
F*iq{$ ,$*, vlLi*h +** +iq-,"''
oh.r'a.y* q-J i9
ry*<k"
,l*- A**3"efu +,+**, +*
,&*'- stp) = 1'*:*it-r ,*|pl*.d ;

Do) : luanti{6 Jsro'** &

':t

apj ) s(r,r

*/ tooo -75p ) -4so *-5* p

'':

-)
a-\
to/ P

2 l'(lo
t*L
-3i pt io $ \ .L *",,& i: 6l*t" 1t,"", supplS

t9 h4+ r,oill av*n*re* ll -)i+,ton

W
fi -t Jrt h4-
fYatt4* at-
(:'

=.t\1 T:-shlaq $ r!)..-

1*^*$1.6 l;*).,&.d
{r^ n *t- ls
q rzealc ra
1*it't \ s*pprj.a*
?

A"s' ]FJ e-.an*€'nd i> A

n"n**-w {t -l"t"q- sotpprW,

+. t1 c.-c-. , ,,^- I \l , .,
P*.1
R''*F.
7-

. ' ,1.: ,.b***n* I

t

*? s*Spl;"{ s *^{ -
qt{a
L
nttlr
++lL a,^.n*i &*^n&d D # l"*l &n* q
Losuh\l
^l
?ar&L ?"*'' !A. {hs* &l{o* Y q"y?q"_
i

=fr"* 0rlt I

5cpy = - 4oe O+ ZooO P

(p) :
t-.
!

w hsrre- p > +1."r_* !- rc t

# 1..+ Jsft,

t *€-_ € ft l=*+*
*A a| -lu- t*:h^tl Whq# i) ihr**
?*..rrr<-._
a1*i li b,+ i \
r.* ,-rr
,l I
I
)
:
Fr-

i
*fr

,'d*t1f

4oao P --- :1'rtiII

*\
p= 1
4
::f,2): *p:L,L: * +BC**y L:
Qoo 0
 -\

(t) k.{"ry.,z.,irnx- -&*o pnl*S',S* v&i"h T;<n {.r'+4-

dr*on.,dJ i) \e-5! --!r^^r, r1FnSi*6- EqF*ii.eJ

Ioooo - t00p

-\

+ P>3
fF P>3 + {+"a.5- I da r.c&r-r d i; t"r} -} n*r.,
>^pprf ,

(? hh.+ do iu
-Jt +he praln*-
Ho* (..',
t*",,.f ;-*rFFq.)
# t.+ & olrt '

.,i i.;.T:*{i+1 3

&**.*-A ,> bs! -l-rI l 4tY"l

'

5,. pplix_{ t
'i
1.*nti1"
A* Prai L,;lt ,oF*
 Ch"
\r. l!5avir*ie*:q Et<.r'a:llrae The price p (in dollars.) anLl the

s quantitl.-r scld cf a certain prr:duct cbev the demand equaticn

P:*:x+2*t)
6
Ansrver i;arts {.a) thrcugh (e}.
{a) Find a model that expresse-c the revenue R as a function
ol;. {Remernber, l? : xp.)
:
(b) Whal is the domain of B? 3

(cl What is thr revenue if l5{} r"inits are s<ikl?

1d) lYhat quatlitv -r maximizes reverrueJ Wh;rt is the
maximum rer.enue',1
(e) \l.'hat price stroukl the company charge to maxirnize
re.,.'en Lle?

C) -na rd€ v€ l-iir e i9 R = yf ,

I

E i(+z
\t !'*-re e- I
r-
-', R t:t-),= X (- * X **use)
*.t*+aooK-
.''i.

(u 't
e e +*?{},*

i ?(=-[p+-fseo 1
' ;1

,-
f\ i

Sro" u.Ju ?( fta+\xc :c rr"i-: t'.

deBr p. --r\.$&f*
ft &"
tl

"-{

sl- *ii.r-
rf;
j o - ,+-
rLIE ,,
t' ;*
:t d ) k* h* ** x**
 rj
-6F* tzoo )o )
re[4t*4.* pria&-
i5 poti-lirc.,
+ (p g l k.**
\
.\
F3
%' F }O

D"nn*,in : {fl € R:
6{PS eoo}

R (eso) = -* I(25o)L* zoox:So

;:? Ii ti,3' l: e
f_,
g=,
[t) Rcx) =. ] * +23ort

*fhr- *L*tt$.* R i; f1 *X"t-r-.:.d f -i cl *rc- , .'. orr = - 16l b= zo(} ntr:t)'

a{, o -['f^* ve-n*ey i; =]1ne- h'1u"-s# pain"l*

,
o.h,. *tc.- p ab a\,t .
^tn
GS*
Gb
I
, Q(E - - --*"*. !5)
Zor qrlxL
r-o
i
^1l.!-$1a-ge
\tz\E\tsi rr'trr.*.r
, ^ -T\E- rr4YgT!u3- l> Wlte-r1 rt;- b2q
,' 600,'F*od,*,tf ct*;€ go$,

-t
 \el

!.?
r\ KF
= ff ,4.p *f on)
- -
i-fsr
*.F"+teo{}
il
! rl .' i
,i
" leot>
3b

f
F---

- r&o
?-.x t*g)

\**

ai
i

! ':- _
 { Maxinhtng Revenue The price p (in dollars) aod the
I
quantity* sold of a cedaiu product obey tle decad equation
l
1

P:-:x+100
J
\
(a) F*rd arnodel &at expresses tbe revenue R as a funetian ef x. i
(b) What is tLe dcmriin oifi? l
(ci lifhat is fle revenue if 1&0 units are sold? i

(d) What quantity r anaximizes revenue? What is the l

inaximum revglue?
(e) What price shoold the cornpany charge to maxir:ire
revenue?

'4'] = ?LP ?= PYfieI-

p= - E L+looI
tc=. rrurnberr dF
pra odtle$
Rert) :- ?( X t 3
x + too)
a- bt )Ll + I OO:c
ts

f:-!"* roo

=t*
? :c.= 3p+goo
9.ca.ruo L foapne 5.nt -{+\g *LrA*n+ittr *& * p"le:**.e f--
*old, I'rnv e- . 1(>o
', --;3p*aCIo !O
+ 3p 3 gao
=) P{l'4S
gl.al t*
i
rc --
=># ' 6elli'"0 F*ioe- i5 p*s)d uer ) $r] ,F>@
}c*ainr t a<pS,oo i -]

t
 tL

t ,r'* loo L
"!

Rex) {-'-

ft{m*} a -'tf t*of' *_*oxr*E

r - "i
!'i

,si d&60 ,( X.
+
fr
V*v

I
@ Rcx; x-e + t€)s L

t b- tao
r-..

- '. re,t{ ey is *l rq. rr;6 r^e,-s* pai n*

qi I r^r* y^**bd*,
:
t
ft=- -?
La -F,- b)

**, *{'1^.c- \"€V&Yli#-* ip scdxin-rr.x*l l*hen IFO,^*ii5

q".ae. scsld
ilJtF.!
,

rn -ra€wyrgr& r },.
w )
,"16)'f ! rnL{
S= -IXatlela+r**s-Fs*

= FsoC * f_*n.,

@ R= ^--P Pq.3 p +str$ =" -*. B$a * A* * f

t #t
*** s 5p4
*1
Ex(-$)
i
(. Y",
rll
j
---

t
 5, Maximizing Revenue The price p {ilr doltars) aad the i
quaatity x sold of a rertain prcduet otrey the demand equatior
x-r5p*1S0 *<p<20
{a} Express t}re reveriue F as a fulction of -r.
(b) Sfhat is the .eyerflle if 15 snits are sold? I
(ci What quantity r maximizes revenue? What is the
mgxinrum reveriue?
(d) What price shauld the ccnpany charge to maximize
rev€nue?
{e) What price should the company charge to eam at least
$480 irr revenrre?

frr x-p
)1= - 5p+ IoO
?-.-)(+,oo
:-. ,'i.. ',(

) r, t *r- ze
Rt^) xx L !*+ 20)

5*t+ Lo1q q-,

i1 ,

Q(rs)= .bxrr:7. tLo xt5

2ss 4 )

: : -I*,*zot<
cl- - I b=2*o
€?3

",.: :

\l

Ylxi * ix* \-re.vayv.e' .i)

g- -ircsqL *+-oXso
= soo $

*-,-}
 R. =tp
?L= - 5f -F toO
R = pI GSp*loo)
\:::..-.
= - 5p* {*tOo p
t
rr&=* * b sts<:

F= * 2a
b
?i(CgJ
*"+

-$trt*too o = *so
-3.€i

) Po-2op +e4:o
:) 136
-d , = c>

*> b.
l{
*r rlqp:f,):o

E\-
r=- 6D 0 \ru
L
.t
P= l

5p p vai*a- Shr t*d be- b.eFw €s n €$ +n tq$

{= €*x,, o *d k*s* 4ea X; n 8_V Q*y\,Lle__,
 Enei*sing a &*eta*gellar Fiel* David has 4llij vards r:f fenc- \
ing and wrshes tc enclr:se a reclangular area.
i*) Express the area,4 of the rectaagle as a functioa af the
rvidtir !1/ of the recrangle.
(b) Far what vak:e ef Wis the area largest?
{c) Wh*t is the nraxi*uo area?

1Xu -.lr
@ 4vatl Aba- -Tc t. :.,- hapne*and +""- \.^c

I e o i ma{z 17 g-- t rt.s__ .a € eh *ek'

r,r ( r> +t.< lcsqiln aryl d \^I l: +'"{-- .w\ &*-h +ld;n
( 1

2(* ?w 3
I :(' \3o *2-w

+ N = -t^/ i+, ?-11o

An"^ ) A"= { x'*
(*w -r
=g
= -w?-* zto \f./

?-^

4tw)'r -hL*?-cr6*

-b zqo

0 '1Y^yi**r.,
24 zlb,) =
i.'LO
w
dn€6,\ - - (i?-o)t *LloYiz,
= l.rqoO
P-"
 S. _ r' - -.
available to etrcl{xe a rectatrsularfelil
(a) Erpress the area -4, of the redange as a fiffitiisn of r'
*'here -x is the leri$h of the rectangle.
(tr) For what value of .r is tbe area largest?
(ci E'hat is the maximum area?

Gr$ X :+ -lt""a- lanXlt" a,"., d w D+IL

J uo ao, q-|o,. ulanru *ueir
"i n ,

2t+- 2w =_ AOOO I
"-i ?,,v= }il.*ar*?K_

1 lgco * L

,Atr r^ .,
A*xxw ',: l. -.

T v ( rsoo - )c )
t\/
/

:-xe-;f50Sr*

o I1 .\
-l

4= -! , b= |SOO

*- x: =!-
i{4

o /- -*{*rso$1,
- {:sdr+ r}oa Ff;o
542 soc
ff n^,
 Enctosiag the Mosi Ares with a Fence A farmer with 2000
melers o{ feacrag wants to enclcse a rectangu}ar plot that
borders on a straight highway. If the tarmer does r:ot fence
the side along t}e highvray, what is the largest are?thaL.an
be e*closed?
'_\ \- -i
\ ;!

(qi $ 4l- t<r-qr+ I Q ,^" d

=

&lU \tI
-,.- '
, -{1-ran '"-?
(l

zQ+w: {,oO, E
'r

) !v' ; QpD - {{-

fu"^ , tl
A
EI
Xxw
= XxCppa-N") -\

2oa? - 212*
'- _ _t-
t- ;

A *
n: -*lx--|-?ICOK
,^flL I

t
Q=- b
: =-*-
200
50
Lo\ 2faq =-

A = t zX 5oa-l 29oX5o,-
: $o0O

-,
 8.000 - 2x

Qr) 1S 1eng{tn =S, ,**d *;{4i* : } ,lt^cn

2x+ ( = Boffi

+ A=€ooo-?s"
,4*"e,,frr {, KX.(
= KI (*oe5-2r0
= -2tl + 3oC01

t - e ooo, = pooe
?l c?)

4 : *?I (roCIr)t+ g
E B OOO AoC)

&-

t.
 C@+"ro - g,g
v l1 q
5)

{- !
(") {repr ?(<-1 and )<- > t,l
-4 -2 Z x

six)
(b)
fx t, I
t -t3.?rSt I
ti
"i

ia) s(-r) < i.r

(bJ ,{(x) > 0 L hraorn -"t !,.s.-
fr*qrE t
\

e){ (EK', -L(x< f

v
{-2,
I oic ot t

2)

:!"
Lu; { reR: 1('<-2 a"n-d L:>J
I
-4 4 x

*4

(aJ ,g(") > f(r f P'o'", +r""- q-*"p I

(b) /(, ) > g1x

o\ 61

,r(-L
+ 3z - lo io
L"* I rne6'lhq., &.r.; rc2-+ 3rr
= - ro = g
?s+ 3r-lo =o
* ,te+ 5x-tt. * re s, q]

* x (r* s) *s trr*5) *,*

* c )L+5) C x_- t) = er

- ', fC= -5 c^^^d X*=, t_

.." 4-

Seo) = oz +3 xo -lo

j )
c
I
F
5
T
I

\ {or- ro)

Y
.j,B
-i, (
L+t?,-\)
( J I X -f' -::-z )t

t*
 @ f-lx )o
L"$ t **Q ir,.a-i iO
"r1,1* 1
'x(rt*'t) =o
{
)C:O a*d }r= t
,i,!
"*.
t
.!
t

to,*
3 1(-1- 1x Y\ {q,
ld

?,{= f*2'r",2. {*tL-t (u r'r)

+ a= (x- r)t* tl

A+t *
(rrzP

a-.r i

f ?LeR: zt(o d x )t
)

_rfu_

1.

-dP
 .L4*i <o
L
xbI e-*
"*: ;
x+"* ck- * =g

:E= -.[ . **r^,{:: L

T,

"I<Z
d- :

L-' !

+ A+r )rl U,-t)

r

€ffi i *t {x {
F
a

I
?
{#o,
& rrz*rc*!Z >C
@ */

L+ t yhsq hF* rta+x = I ?-

+ trl+rt. ^tE =s

+ -t,L-{cra*3x-t?:c
.1:
:*) x{e-i .r} *3{a**}.a
ii
s) q"- x-"* * ( *- * *,e]

.'- ? r, - *1 **d ?($, ff

]
 I

I'J
trF
3 ?LL*-rc -L l'L

+t= rz+ ?,rr{+l*)L '. - t .\ .\

+ 7+z+{ C** i)'

iI
= c
&

a
€-

) X+q =1',t+*)L ;{' '$

kt,-
\ )ttffi" : rt(-t a^,,d, x) +
 L* < a*sx

L"+: i *ft t\*e

a 6rtl Sr<"*,6 e^S

? 6*L ?rq+tx*& =cr

? 3x-(Ix* 3) +z(z r-3)= o

\rr.--?
6qf\ql.ftr*
s

.:t?GRr -.:(x.il

&* I
I

3*Aft lns,- **-- i

**"pt Hsu.ft
tl*{+ . I
s qL{.1 i:E t
?(Lx +t So
\i-
:

4
)^a_ ?
1Lx {*l -*Q

- b* d L+- tac.
* il
''...".-'+"

{-J*

t *r)t+ q.f.!
=- t'r) E1 €
.''r G

i*
-i :' fii "i {r
t
kr $E-

I *{ -: te.

,r a.rvr d t-s
+.

t'[o o*,,rl 'SoI. *roayJ

t

,#ft,*
*tu=.* 1
 ?S*z +l€< tOr<=
{} tsL
,IEeo
+ )-5*r -{ox *-}& < S
&-r
H

Fr
& t**
re
L 5*
+ LS ez- LO r< * porc-l-t6 .
g
= k*o IE
.I
F
4 l r.e++ f
€

) SrcQ.o- i) - t (sL:'1} "-o

* Cs*- u*) u s- I
+ !
i
S-*
I

e Tlff.- ,$qu.*tg*.

be ,r 1"ua \?€q \ S. l.-r"fi .n

kJ _?

t'

r
 { (gae- a*) >-?
l
.^'...i
atrrz-Ar<.+) 7o \ ii -*i

+
i.
Le-ft lrra4 t t LJtt- fu"+? =O

No w*"r\ ,$olr**,on,

_M

i: -\.-

I
 @ w hrJ- i> =fho- ao*o rn o$ +1* {,**, o

+. )t) = 11- \{ )

A*t;
t ?L€ R ',
t o^^d 1\l -4 ?
I
:

V* )

In Problerxs 25-32, use th'e given fwnctions f arcd g.

/ai So/uef{xi : 0" {b} Salveg{x} : B' {c} Solve f{x} : e(x} {d} Solve "fi-r} > s.
{e} Sotve g{x} < 0. if} Solve f{x) > S{,i {g) Sotxe f{x} > 1.

(^\6

+Cx) = )L'- I

?
(r) = 3zt3

@ x2-l=c =) rtz=[ =)L=tl I,hF,.{-t,*}

G 3x*3*- o+ 3x=-3 * 'rca -| /+"n, t_,\
e {c*:= ?rx)
*tE t ?- 3r+ Q

x2* 3x -t-]=o
-r1
:!
.Lt
t.i :
l:,'
:
J

* 1az,t*.{x- t=o
t'i i

* tL- q) (rt+ r) =*
r4; a*
t t<"= -, I f lr t t 1
J
 I

&t >o I

I
3='uo-l
? 6+t =x}
I
I
l

ir r
I

i
I (*r-l
I

1C€*.: t<-t a^^,d )C>t

t
E

i llnsz

I
ft
T
3
?= "*f
ewl x
\L
.\

r €{R as- t
)

.{-}At)q =\.

i tt*tRl x4-t'**d xr'r!

*
"t ?f cx):4-'

A4 II

ffi r.Lr ) r
) * -Lz o
.l'r t(a-l :1 l-

,',{r1*R:',LS-'tr1 ^"d rr){t- )

2*=!
+ 1=tJI,
Qr/