Pat1 ตุลา55 พร้อมเฉลย(2)

:j'-

Yad

todounflietfllflet5 (PAT 1) q61nil

i.

nfisr PAT 1 ma1nil
q

1.

55. I

55

rirrauohi'u riluronnvrii'ufivrf uac'lri A, B uas c rflu#urryoaar u :iatqaiolildanoioo
(PAT1 or.o.55)

2. (A n B)-C=(A-C)n (B-C)
4. (AuB)-C=Av(B-C)

1. A-(B uC):(A-B)u (A-C)
3. A-(B-C)=4n(B'nC')

oOU ria
rirrauo'lrip rar q rflu:Jfiflef :l:n^rofludalooiotldritu#ofiiuo{ (pAT1 q.n.s5)

1. (p=q)=(q=p),
3. [(pn-q)3-p]=(p=q)

2. (-pv-q)=(p=q)
4. [(pnq)=-q]+(p=q)
moil

oou

a
I
v{0'1Til11J 0n?''l

-,

1a

1Ja

oou

?a

U ,J

il0 a L!1*

n. ri'r p, q ttos r rilurJ:vlror.iToufi p = (q n r) frri'rorrruoitufluoi.o
q) (- p
ua"'r r
=[(p = ^
= r11 fieirn'lT ruailriluo?t
u €a
J
I r
?J. fl'llll.tot0nRilfl8JllYl1io0 {x e R x' < 2x + 3} [eJ0 -a n0LtoflA.:01U?1t01.]
R
I
ud'r :x 1:' + 6 : 33-' I firirqrmaroir riluoS.s
rialoei a't:Jdgnoioo 1eRr1 o.n.s5)

1. nnRuaytnn
g{

2. n nn uoi:r fio
q
+. nfioravsfio

g. nfiousirnn
{

4.

ritauotrd I ryrl.ufiora+irururfiru lri' a
trng

B={*. I ll*'
tt

L

={xerll2x+:l<l;

-*-rl, r} fior:rxrfonerilsialild
t )

n. ,iru'luarrfnta":tggr
u. A-grilulro'ir.l

ann

rvirffu 7

riatoeiot:JdqnoTau 1eRr1 0.o.55)

1. n {!n

uas ? an

g. nfiousisnn

2. n nn uEil fio
g
+. n fi'q uns I ficr
I

r'- .

2 {oaounfinnran{
s.

(pAT 1) Earnilss.

d'r R rilurryorrirqaura{aailfl'rr (x-2)xz+2 q(x-212x+ro rfio x > 2
ru#r R rilu#u

1.

rsosar?ir{ludolosiolild

2.

{2,3',)

(PAT1 sr.n.5s)

(3.5,5)

3.

(2.5,4)

4.

(4,7)

oou

6.

rirnuo'ld'R ttaurssrro,:*iru:uo?.: urnrilri'I rrflilrsnsa{,iru'rur6l ld'r
a1R R

tllril

n

Tosii

f(x + 5) =

*' - *'+

uor g-'12*- 1) = x+

{

rrns g

ria

rilufltfld'u

Zx arui:.lt1n'iruruo?.: x
q

ehuiurln'iruruo?.: x

fior:nnrioorrilsiotild

n. (f - gxo) < -169
fl. {x etl {s.rxx) + 5=o} rilulqfl'jrt
riotooiot:JdgnoYao 1eRr1 a.n.55)

nn
s. nfiorsiran
1.

2. n aR rroi:r fio
+. nfieruarrfio

R nn Lrn& 1
sl|.u

q

oou

oau

7.

a-

^

fl1fi1.[o[14

l,a

oau

1Ja

I
,-2-cl e
r=j (x,y)eIxl y= zx. -u I rfia t ururrnsot,iruruudru

x'+l

t

'iru:uerur8nfl o.itssl

1.2

8.

da

Dr

J

- R, rvirn-urioloeiahd

2.4

(pAT1 o.n.ss)

3.5

4.7

fiar:a*rriaer:rilsialild

n. cosf+"or$*.orr=1
tt.
eq

,*ff- t*+ = cosec*
, U,J

Y

t!flonoa$
1. n an o*r', un
g. nfioueirnn
{a

LoCIa

(PAT1 a.o.55)

2. n nn ursis fio
q
+. nfiqunsrfio
I

Yad
o[odouoolofnffetS (PAT 1) Ea"lnil

?ia

oou

tia

riatoeiatJdqnoiao (PAT1 er.n.55)

1. cos75' : (2 - rE)cosl5"
2. cosl0' + sin40" = cos20"
e. fir R rflu,irurua3.:'loq' uii': *31 cotA
+.

10.

3

sou

e.

55.

cos2A+cos4A

cos2A-cos4A

ri'r R uar B tiluo"'ru?ua3{'[01 ttd'? sin2a+cos2B = 2sin(A-B)cos(A+B)

*.r..* = arcsinl-

rYi

z,,,ccos-2 uii'r cot[4+arcr..*) rvirriurialosiot:Jd

JnJs(2)

(PAT1 sr.fl.ss)

1_

^ 13
.T

_13
g

4.
+'

3._13
16

11. Ltnutanro{?tiriluthu:ra.:r#r.lsr:lfirdarJ:cfi'jlnqosl-olto{l.:nnil
I
,

x- +

2

r,s

y + 6y-7

A

a

= 0 Ltflsly{ftflooilflfl0.:x.:50Ei!ilLEfuqr{

i

13

16

* y'=

25

riurtnnn
a

x+2,13=0 fliln1T10':?.]T

m:rn-uriolosialild (PAT1 n.n.55)

t. i*4y2-}x=O
3.4x2

2. x2+4y"*24y+20=0

+y2+6y-7=A

4.4x2*y'-32x+48=0

eo! fa
12. ritauold'n urrursodlnauta{drJnr: 3(1+2x) *9(2-x):z++ ud'rtqfl R rflu#utrqrot
ri:rloEiatrJd (PAT1 sr.o.s5)
4. (-3,0)
1. (-1,4)
2 (-2,0.5) 3. (0,5)

oou
13. ritauot#n

rilulelsr?ndfififiG

:*:

Lrou

ria

6au

?ro

de(A)+o fiar:rurrian'lrrusiatild

n. (de(A)3 = de(adj(A)
s. d'r a2 = 2A uii': det(A) = 2
q

I

e
, U ,3
datooia L:Jilo.nooo (PAT1 q.n.55)
{

1. nanLIEi?lan
qr{s
3. n fio uoi:r qn

2. nnnuei1fio
+. n fio uac I fio

,

4 doaounfinqran{ (PAT 1) Ealnilss.
14. ritauolri'P

= 3x

* +y rilufl,orifuno:.J:ratri-Ioufiasilnr:{odrn-q eird

2x+3y26
2x-y<10

0<y(x
fior:anrianrrueiotld
n. p firirrurnqorvirriu zo
:r. firne (a, b) idfi1td'e frriroirqo uii'rqo

-

(a, b) flaornd'0.:niraunr: x

y=3

rialeoia'lrJdgndoo (PATI o.n.ss)

nqnras?Jnn
g. nfiquoitqn
1.

2. nqnueisfio
+. nfiouncsfier

oau
1s.

rirrauo'[r{

d,i

rlflv

t,

rirrrntEraf w rirruru
q

arcsinl
----

Jl

rrnrmaf't ud'rrirrot

1.6

rijurrntnofuu:yuru dt u*v-fr,=0,
n-uurntoof

I

unsl?ntqof

*

i'w=8

rirruru

'

uae

i'w=-2

,-*.rtr{

J,

n-u

II12 +Iv12 rvirn-urialosiat:Jd (PAT1 er.fi.ss)

2.10

3.14

4.18

osu
16. ritauor'lrinec
rlil B raer{rJ c

ria

rilug:.Jarruru6uruto1 ri'r a, b [rns c rflunr1ilur']go.oqirufl:.:?iraJe1iJ
nrrua{roi:-r

Ioufi

--l-.#= r.}*.

tio

A

ua'r sioc rvirn-urialosiat:Jd

(PAT1 fl.n.55)

n J,
t'22"'z

2. _!_

3. Ji

4.

1

sto!
17.

riT

rauold'2, ltau

'

n1?J0{

1.3

22

rilu'l"rurur8tdaudooond'arn-uaernr:

t,, l'' * rrr,
,tr)f!.!'l

li

,rr, ,z )
2.4

='

1io

oau

da

- g.+4 = 0

rvirriudalosiat:Jd lenrr o.n.ss)

3.5

4.6

lYad

{oaounsrinnrcari (PAT 1) qatnil 55.
18. rirrauold' u, = rm(n,r-i)rLar bn = o.o, [2n,. -

,.rn!?Rra{aun:ru

fr

*r*

])
3l

5

rhrair n=1,2,3,..
ehrail

.(t)'. [fr)' .

.

n -- l, 2, 3, . .

(#)'+...

rvir#uriolosiat:Jd

(PAT1 et.n.55)

2.2

z.-?

1.2
55

4.-2

nou
19. ritauotd't1x)

=

x'- 26x2 + r*-#rdo

o

:ia

riludruruoir d'r d1 , a2,a. tflu,iruruoi't

au,iru':u6utn-uuuuairo-r.,rr:Trnfio ttactfllurirqo]JlJo{flflJR.l: f(x) = 6 rr#rri'rto.: r1g
o,u,J
rvirnurialoda'L:Jfl (PAT1 o.n.55)

1.

211

2.

1A7

3.

101

4.

85

oou

oou

20. ritauold't(x1

rflunrlurrudra-.:aot Iou;i (o) = 1 uos f(x + 1)=

shraf,i,irurua3.o x'lo 1

21. rirra.: ri-

-12

:ia

1

4'

|

i

It+x-2x21 , e ,, ,
[3------r rvirnu:l-olosio'L:Jd (pAT1 o.n.ss)
u

x+l+ {; +3 -2

1.

^
3' i2

2. 2

3

1) + x +

ui',r.t ] r1*y ax tvirn-uriatosi at:Jd (PAT1 ot.o.55)
-2

1.

f(x-

ria

2.

o

3.

12

+. rarrirhilei

oou fa
22. lunr:maqanrsr"roa{anilfarun-u nrurirasuilufirarironrsl.ronudtduuui'r a uasu#rontsir
gsq{q
6nonra*durusi'ru o IoErfi 1
{ab2

1.1
" g

2.1
6

*l=*

rvirri'rriatqrsia'l:Jd (PAr1 4.n.55)

3. I
"' 18

4.
"

I
12

oou

ria

9t^d
6 {ofloilnoretfllfrer:

(PAT

l)

Ea1nil55.

2g. ritauolrinru#rult'u:f'rfirfi,:rifu:vra'ir.:riaruafiritauol#giot:Ji$tflut#uo:.:
q
x

1

2

3

4

5

v

3

4

b

7

10

, u ,l

?0'l:il11lan?1ila0

[]J1*

n. rirarunr:ra{flx1sJfs.Jfiuf,rfitfl.orifu:!fl,j,1{?iaila
:t. ti"t x = 15 ttti': y =26.4
rialodat:Jdqndao
1. n nn tt03 I
{.U'U

6o v= mx+ c rrii'r m + c Lyiln-ll2.6

(PAT1 er.n.55)

aR

2. n nn uroi :r fio
+. nfiouncsfio

3. nfiotusirnn
t

oou

ria

24. ornnr:aautrrofiosraCIfto.:rinGuu#'otradt :J:rng'jrn;uuusouattinGuufinr:
ua n uo r:J n 6 un c dril uo du;nttti'r fuIA.r :l n fi :vwir.: o fi t z o-r qrr:r r ol:J d
oi

z

0.5

1.0

1.5

2.O

1r.1l{Yl

0.192

0.341

0.433

o.477

ue

e

xe

,u,J

?la1TEU11J 0 0?1 il fl A L:J1{

s v

a

io

o

X

n. nlilnL:Ul,tnilfiU{ 1ilfiO.:UflA:J
3.1'l

r.

OTg'l

U

LtaiX 01 eJ1

#r n ; uuufl a uasl
u

d

q

e

X

n

a:g'l Ut

fi

udX,-

A

o fi 1 fl o

v v

{ Os

ttillAfl a U1 0'l un

o!ev,^{tuX,Lr6[i

[T

U

1.tO

UUtml

n

U -2

or
Sr o {#n 6s urio.: dfi rir eirs a urvir n-u 60 o c ruu un v fr
e

t

ilnr:u1l[1114o{uflauleiflsuuuriosn'ir 54

?ia{il

i

,

t

tOqlcLtUl*1AOUn?lO'l$'lUl[UilAHRA{tYl']fl0.1ff1l*tUU.:LllU

flxrilTsAm-iir a{n1:LrilTr.r1ar

a

flvr[1.[1*

<r

a

--

v

a

60riiufouns 15.9rto.:fin6EJu

a{osttuuflaLutytlnu

0.

1

rialooiat:Jdqnoiao 1enr1 m.n.55)

1. n nn
{g

L[or

fl nn

3. nfiouoiran
{

2. n nn ruoi:r fio
q
+. nfiounrqfio
OAU

v
?JO

tyad

55.

7

AEDJ

'[od0unoi9lfl1dst: (PAT 1) Ealnil

1JA

25. 'h"'u6l,iru:u 0,1,2,3 n":luorr-r.i +*+ siotjd (ria.:ar t ,iruru;
a

b

0

3
d

r'

i

UI

t

u

ao

d'or

f irururdru

ttm

At Ltn']A O.:3JO''11{?U[6'J O,

ugi

LO

nsn

v{alTil11

a-n

0 €r?'t rJ 0

0

1

1

c
2

2

3

1,2 ua3 3

o, 1, 2 lLfls 3

,U,J

a t:.lu

n. dha<crd'?b<d

t.

ri"r a

*n

ud'r c <

O

b<dud'rc<d
{, a+b=C+d
€t.

ci"'t

:iatooiat:Jdq:Jka"'qnoiao (PAT1 q.n.55)
1.

3.

n

-

as

: nnLY'IU.1 1
s

2. n -.: nnrfiEJ.s z lio
4, n -.: anrnria
gq

?J0

ql

du

n-{nnL?.lth:3flo
s

I

[-"ffi]
26.

rlrvuotri'u rilura nnl,r#e.nl-nrf'rra;1rf,n unr g rflu#rlsqta.] u

dt

zoo/o

ra.:aurfinturser A riJufimfrnlurqm e

2s% ta.rffxn8nturqo

e uiluaurfinlursfl

unr.iru':urrurfinso.:ugEr (A-B) u

lvirriurvirto

R

(B-A) rvirriu t t2

uit':dT

u:uam6n:rotrtgr A u B

(PAT1 o.n.sb)

stou

27.

td'

*.[**ro*0./:**r
ura;td' g tilutqor{rfl aura{ffiJfl1t zx2 - 5x * 11 * 2,,1 p a* * 5 = 25
i{ail?Rllo.rdlrfinvru.:fi eJq'[urser A u s uyirfiuryirto eATl o.€r.55)
R

tflluttqriroouta{fliln1r

l;i.

=rn

CIlu

28. rirsa.: r..'(2u,.t*] * *.*f) rvirn-urvirlq

(PAT1 or.n.ss)

gou

9rA.!
8 toflounorsrfllflslr

(PAT

l)

Eo1nil55.

zg. t# e rilu'i'ruruo3.:1o1d'r a uns o uilurirrJ'rnqo?Jo: .or4e-sina0 ltar
mudroi'u ud'r a * o rvirrirrvir'lo (PAT1 o.n.55)

3sin0+4cos0

oou

30. rirrauo'l#R ttvtuttflrlrflalta.]flaln1: *2loga1*2 +2x-I)+xlogr(x2+2x-l):2x-x2
uartd' B={r2 lxea} ,{au?nga:6rur8nyr".:uruoturssr B ryirn-!,r1'r1,

(ror,

o.n.55)

oau
A d

t

A

31. d'rrrnnuufitfioogurinnr.:60
"

-. ,,

t

-

c1n, t1 oti:.lur#uor:.:
'
,

a

x+ y +4
'

X,

= 0 uava.:nalflr.iruQo
t

^,

AGs, -2) Lrasoo B(-2, 5) uii'rdufigoq:Jarruuadur ABC rvirn-rrvir'lo

lenrt

o.fl.55)

32. vrr:rTuorg:Jradrfinoaaoaqjfi n1-a, 2) frunuaurl$:flu1rarlnil x uavIiln-a F a{rur#uor:r
I dtfieunr:rilu +x - 3y + 14 = o drl'nmIua'rd'qr-qn-:rr#l.{er:r r- fino B(a, b) Ioufi a " o
u#'lzuagruta{r?nLma{ Ar. FB rvirri'urvirlq (PAT1 a.o.55)

33. rirrauqld'n,

B

rai c rilurilsrindfifiG

:":

Ioufi

aete

+o

dt4=[] ? ll

[: -r

o.]

rLnr det(BrCB-')=-o ud'r o.t(Qtec) uvirn-lrvir'lo (PAT1 el.fi.ss)
9-0u

34.

thfAiU n = 1,2,g, ... fiff4Ufrt#an = 2 + 4 +6 + ... + 2n tldg bn = ?r + dz + ds* ... *

rirro.:

J3i[+

3s. riruuqld'z
rirra.:

* o]

*

*.. .. #l

ryirn-urvir'lo

on

eArl a.n.ss)

rilu,iru':ur6tdaufiaoon6'orriusrunr: 2lz + 1l = lz + 4l

121 rvirn-urrirlo

lrdo z rmu#{qn (conjugate) ro.:

z)

(PAT1 o.o.55)

oou

30.

fireiro-uuo:rofiflrofid.ifrzun:r?n 1o nofrr:nryirn-u 20s u0rrl0:rrn6n to yrar[o-ol:J
q

rvirfi'r sos uai'rzuaurn 5s yrafu:nsotn'ro-::rnrnrflodryirriuryirto (pAT1 er.o.ss)

aou

tl

rToaounfinsran{ (pAT t) qlarnil
g7. ri'nauold'R rvr1.u{qsa+irurua3.: trdt:n J R uac g:R
1. (fgxx) = 2x + s ahraiu4n'iluruait x
z. fitrifu f uff! g fior4n-urfr'r1no'uoiuihrirrln,iru:uo?t x
s. firf i'u t firira.oao#ln-r:f'rvirn-u 2 fi x =
ql
4. s'(x) = z ihuiurln'ilruruo3.: x

I

s5. 9'"

n rilufi':ri'fi'uloafi

1

9

q

du
flrfifu

a

I

@

;

v

d

t

u

r 0

g ilrirairqoaeJv,ryriryiln!tyi'r

Lo

(PAT1 o.n.55)

aou

38. druuo'lu-p(x)
fl11I0'J lim
x-->2

rilun4urrufiaaood'a.:n-r

tF(lr) -

r(g

rvirriurvirlo

P(x2 + 31= 3xo

* 24x2 +40 [L6t rix;=ir6yor

(PAT1 er.o.55)

qau

39. rirr uold'e1xy

uiiunuurru

loufi

e1o1 = 1 uacsaonii'0.:n":J

3hx + 2h
lim
h+0 P(x + h + 2) + P(h + 2) - P(x + 2)

-

P(2)

=r rirrat

P(12)

rvirriurvirlo (PAT1 q.fl.55)
CIllu

40. lri't-rilur#uo:tfihiruoo(0,

1) rua;ote.:arnn-:it#uo:.o

x+2y=odufito.:u3t':rx

luoraoiud'(quadrant)frtd.:#aa.r:o:.tsi'rrunuxttn:![nuytfr'um:.:Luacu#uq:.i

x+ 2y = 6 rvirn-tifrqr:rtmilrtJ

(PAT1 m.o.55)

oltu
41. ritauold'n = {1,2,3, ..., k} rfia t< riiudrururfituan
rraclfi B={(a,b)eAxAl0<b-a<7} ri'r?0.: r rvirn-rrvir'lofirir1ri',i"rurueilr8nra.:tqo

mtivtlu

B

(PAT1 sl.n.55)

oou
42. ld'x umu,iruruarrno'n abc uas y uvtu,fruauerilua-n coa Iosfi a, b, c e {1,2,3,...,g}
rar a, b, c urondrrniun'oru, fir s rilurror.o * ti.ru, IqEifr x - y firi, urnaor
ruii':

zu

aurns

or

ailr8nturso s ?f{r

er

o ryir n-u

rvirlo

(PAT1 er.n.55)
CIolJ

42. ri'rx,yrtn;ztilu,irurutdarlrnfimoond'0.:n-ux+y+ z=16, y*'=xtBt')uas3v=3(9')
urii'rruanam a.: xyz rrirri'r..r

rvirto

(PATI o.n.55)

oou

Yad

tofloilniiletfllcrer: (PAT 1) qla1flil 55.
ilv dt

fi

r

ouqri orirt#au

44.

1

tlJilJ

rin Guun

fr

6i
9

o eru d.:

risi

avnuril uam8nr

11

o.rrilriletlnl: rtareJ:il fi wr utarru:n

ttarvr:J'i1

a nu rilumrur8nsa.oser:ritrnr:

fr to ou riJuarur8nrarrr:rfiwr
fr to oru rfluarur8nra.:rer:ilousri

fi o eru uilusrur6nro.:rer:ilousr?runctilrsJfivn
ft s eru riluarrfrnro.:tru:ruitrnr:iunrtru:rufiwr
uarfr

3 ou tiiumrurBnta.:rr:ruit1n1:tLnEril:ruouo3

d'0,:nr:udanr'irr?lu 1 01* ra.:usiarrru:uloufirrsincnurlt"'a.:tflumrur8ntfiu"rteJ:ilrdurrvirrfu
{
u

o

a&

,

,

^da
drururI.roano.tnfllzilyr,lfirJotyrln:JLvl't

q

Lo

(PAT1 o.n.55)

aou
45.

druuo A rnr B rilurnsrnr:nilo

0.30, P(AnB)=0.06 unc P(AuB)-(Ane)=0.:s
P(A - B) rvirn-rrvirlo (PAT1 sr.o.55)

tattuqnr:niE
ruri"lriruar

luutruuilaar:-Jt rnsdrruold' P(E) uvrun']'rrilravrilu

l

d'1 P(B) =

sE!-u 0.14
46.

va

;

'
rirn-r tgs
3A1U?UvlLtglnol':XJ1:lXJnUilrin5?ilt: d'rdoruarodfieireilsoru unr
! I
-,t^r,"vx,#ru:J:sRvrGla.:fid'urvird'r o0 [LdE o.z orardroiu uit'ao':rruuil:il:euto.:riorunsofrrvirnu

U1flAilfl

rvirlo

@

(PAT1 0.n.55)
CI_Et_lJ

47

.

0aa6uA
'Lunr:aa::itrqrrflflaraofror{nl5suoo.:ri'a.: :-Jmng'jr eirtadutarotfiorrotflsrtuuflau

ryirn-:-r
u

a

os orul*u rinu3uuli'0,:ur:nfr +o ou ri'a.:firorfirin6rJu go ou d'rnvul*ufla:Jra{
e

au

t

{

^
unL:u1.rra:u:nru#er:-l:vRmGra.:nr:uil:zuIuuvirn-:-r o.2u1?-r

6s

flrLr1r1.r

dt

v

a

y

ytv

n riiuti.ntTuutiotu:naor'Lt;l"'

6ouilurimrrqr:orurvirn-:.r 1.5 nruuudorsorfnGsud'atfimo.ofirieuifiu.:r:ru

rurn:orurvirn-:.r 12 nvLruu uunvu'ru
4
e.rrm:qrutvirn-r -z rrii'a uru
&

t

r

rflurinGuuli'orfioa.:aartd'octtuudorilu rir

mor'lsi'frflrLLu1* (PAT1 n.r].55)

oau

lYad

12 toflouootgtfl'rdgt: (PAT 1) 8a1nil55.
48. tunr:aauisr n fi osr aorSr a oin 6s u#uni

s

ru6n

:*rflifi o fi nrtuon uo.:

nsuldl,t

40

10-14
15-1S

50

30

-24

d

o'ruru (ou1

5-9

o-t

20

20

n'rnsuuurodurarnfimria.:nruuuarudrfiEJuluflJ
{b

lqgd u < b uoe u.i.il. fla{ a un; b lvirn-u

t+9

rda k, a

rn! o rflu'iru':ut6ruurn

1 u#reima.r k + a + O rvirrirrvir'ler

(PAT1 fl.n.55)
ctou

49.

rhrir n= 1,2,g,
qtnthururdsJurn

...

n

rirrauot#

drlrtf

un=r**-{ rrar o" =t-+-#

#ffi=rrr,

(PAT1 0.n.55)

osu

50.

a'1 a,b, ce{1,2,3,...,9} tta:aaend'arrYu lsf xa)+(7xb)+c=416
uf,'l a + b + c rvirn"uryir'lq (PATI q.n.55)

qou

rilau PAT
A

-

t

5s n A

n.n.

(A-B) U (A-C)

tBUC)

-(Buct

A

(A-D) U [A-C)

#

rio

(ANB)

_

Ln-cl n Io-c)

C

(Aft
2.

A

I fin

- (B-c)

s)-C = (fr-c) n (0-C)

n t B'n c')

A-(B-t)r'An(B'nc';
"ris

A u tB-t)

IAUB).L

(AUB)-C +

to-t)

Au

+

Ya

1J0
dtrJ

O

efin

ioB

4

'.lfl

nor-r

q,n',1# U""-U",.*
n""1'
frûioni filurl,,^qiufr ,,r,rro',Jrrrohruo frranr nl',e.,cit'lr,fro',trr
'1ur3*
'.,
,',1,*,fi q riil ur nt mr *.illuq-:r
6ul-or rjtrnlillv,nl
rr ar nrqdo.r{ r ilr,*,rlru?lr.rfir iriudr raiol*,l,i
âl
lfr,lui ,i*fi, irlu fila{u}'
t?
iou sr or n:'o'ii i r fi Fl {o{et ti 6 r #ori
'uotrl *nnrl cracr trA-1Aloir { r,?n do{nn 6r r,firri fr rtin tr{n: i', dr,.ôrid1oiln",ru"riu
",,nol"o*,^.',

'

(P-q)-+(1-P)

ds1

{o

(-P v ^x) + tl -t ar)

L

_/ F'-

't'(P

TF

Ar

FTTF
.

't-cf

J

q

rrrrfr ,lnrôlrili

fi urfl

q

t.

P

F

T

F

I

FTF

/r-t/
Y
T

/

-=F

^

'^-

"iri{orr{r 4tr,,fixirfrr

(p--+n)

q)

,=T

Y

q;nrh;

tl

utl lii d

uil r, rfi

r

6,1

/

"

-t

a,r:-;-?-'
bu"fntlul 4lr,rlutr nt

4,t

/

P=

r, n=

$03

L(Pn^%) -+

{s+

- P 1 --+ (P-q, )

t(pnc1l

F ----

TF

-

+ (?-X)
7
-----

-,1,1

TF

F- -, C-B
d-, "" i,,rtr*r/

'fi,.-=-l=7

lri'ilrlnill

rinu6.r
v j

d,

C ou

t r nr'l fr rjr

I

toultltI dlulufli
I
I

Tti.k

TT

fi,i,Jrrruqrl Yv//vz -+

I
I
I

lN

?tr,-umarfi{fi
o,i

.

^

P=t

,%=Y

Ii rilu lfi q

frrrlfr N:-r

rxAr01r1tf,ounr'rxniluflrf,Y"oi

, W=

frrloinr nirruqir.us,r]rrnririoz qrnnr:rlr Na r r,Lir lfiutntmrtrlaqtnila:H1r|uuu
r
ItJ

11

t

unufu V/////A n
.:- TTltlt) =- T
1

Vnn =
IE
1ts

1

2-

v

"Uo-}

1ro +

(P+

cl,)

-

!.

(1+ P )

n)

11n

rr'r

(t+r=r)
:T)

d

nrilfi rljuqilotiirfrua ( F +

F

:

:

t'lr,r,iluXrt*ir*Jr r

T

= (-TV-F) = (FvTl = T
uhtr Ltpn-q,))^? J= ltrnr)-+r] = T*>F

tJrlriuilrnixfi t
=

r

tin{ LtpAX)-+^1i; L(-rnr)-+Tl: F+T: T

L

ril.r*flrilludrl

tluuiludruir Al

3 *

rnrr*r4ou 6rcr

p+

A

/t

(P+r)

q,filr*q'i,16if,r,oifio

i,'liuq't nd;1lii1 [P ))= T , (P )Y)=r frrfl
nnoitfinnr3olfrl4 n riu t'r.lr*l'ur11nfil

rdrlfrtautratrounrJtttn$11 qlti q)1) A (P+r)
nt,.rurdtdrrrair,rilorru,o v uJiuHrilu n hrfi

(t^r I nri11s -+

rrmfir

(p^n)+r

'--)

(p+r)YfP4r)
A ulHuxliuV
:d,fi",,irioudrroido f,',1#',lr,rqrjtfr'u.,^l*?.fiJun1lfro
4

dt

I ,

tllul* lrju [n c

(- PV -%)

p, (XAr) - tprl)

Note:

I

trnx

TF

6-101-l

1 v

X=T, P=F nilrllu (Prq,l= F-+r;

tF
Lfpnl)+-q,l -+ (?*q,)

^4

dd

i,rnld

TF
t(pn-11 -+-Pl'-e P'a q,)

, ,n J
dIil'l)oil

LL6or{nio

F

TF

(^pv-q,)-lpaau) i

G

"
tiAnl it t nn nl6r4rlnl[u uI

I -xvx zT I
I
T/X A = % I -Xnx = f
I
.
F V m = Wh I X--x z *X i
rAW)z I lr-r-r=F
i

lriui{r- TV m = f

I

i

urjnr^enra
XeyE-XvI

r

]'#,Jt,^q,ifidnrnntxflitt',]u,fl.
d'oP

merkrraiudrill?rrn

-Tv@zt

-T4@'-@

-XVX;T

1A la = @
I -t (- p -+ r) J
( =
u ='wrv(-P+r)
=-FV(Pv17
= (-rV r) V
P

= Tvl = O

nluuR

nn,frett

1) l1n LL-- [xeK I x1-. Zltl]

[xeFl x'1-Lx-:l<o] = ixern l(x-:)m+r)-<o] = {xetR [-t-<x<3]
r x
1- -, -f
?tn?sfrlqniroxnlfin'inlt:rl-lrro: ]xIr'+ [= )3-x ] tilo x t w. { - r-< x-<3 , xe RI
q1n ox+b = 3i-'d

i6i A+b: +
It
dt,-{

[1.X1J]1

=

{

J 7

1€ (.l

3{=A

,a ----+ tAt?)tA-3):0 --+ ff "3x=fi,1 .+ X"l
d,rdr* {s l. nnolol
lx[:xt!'33-]l = t
3x7o lnreR

At+gA -L1

--b

fill]lL]

,lve'

daillouotsu 1. x

fiqrtnn A : l1n lZx-t..tl<1

Nq1:6r{r

-1< Ix+'1 -<1
9-l .< 2-x < 1--l

iiun

qrn ll'- x - r

B

x'- x-1 z 1

[il1+

XL-x-1 < x -x <o
x(x- 1) < o

u

x'-x-L 7a

1

2-

u

()(-z)(x+1)70

-16 {ZX< L

71

I

U

- g-<X-(1

tA A=t-r,-.l )-6,-s, ,0,1]
''t

"
[ 6'l

t,
t,fl

-f,-I, -b,-s,-1 r-3,'Lj
A-0 = t-1,"0,1r2J / O
An g = t
-

d

l,

rilit0u010u

2-

< 2n i:dtrlir rn <
ant < a' q:6rdir m 7
^

n

ncrolio

n

firrrfio
lX- 1- )

1) cr <I-2<"1 --+

2<

l*ifrir rltz

(x- +)u+2) )o

nr fl6il1st o 6Nn1tflfr

v <

orotrlllt

0,[l

Z

qrI dir

l

-, 5>Z

1v

bn

--r x>3
xL+L< L/,+10
*'- r-x - 5 <o
[X- 4)r X+ t) < o

-2<x<4 n
11

<x<+1

f

rn)=

X

>3

"/

13,4)

6rrj{0il n or

d*lrria riurnufllidu?urroi.(ir

2_< 5

n r6B

x- L>1

z)

2 <X<3

3<X<3 "

5

5z
lt
3 ). (*)

l, e-)

o

<3

3

rtu

o<a<1

g

flfr (3,+) c (2.5,+)
I

n

L

ldx

1

x<3

> zx+lo

16i ,,<-L u I>+

?>

zX+lO

xL-?-x-B >o

r"fer

1r

x

x'*2
od:rnr: (x- z)" ' '

fi

n" nn
'!

110

J

a-

iiriaiu

+ h(AnB), Y
s X" sJfl

y<

3

x

frr f -'( a, r = E

r'l0iir

{1n g-'tzx-1)= x++ fJsiir $tx+rr)"2-X-1
n) tf-grror = fro)-g(o)
= [t-s )3- t-s)"+

2-(-5)]

- [z(-+) - 11
. ---

(-125 - 7E -10) - (-8-1)

(-lto) - (-q)
-160 +1 = -1E1 /

-111

a

-Y'rftol 11nn1rt!n.,{ X= -5
lu {rx+s) " x1-t'+zx
- 1r1 9 (o) ilnfh,rrnu X. - +
q

l,u 3(x++)=Zx-1

-1/c
., 110 n.

,J6-l

cU

)

dxnrt

A0 t111 g'rr oror:rol

t3"f ltxl + 5 = 0
r
g(t(x)l - -5
lv
l,rnnitcrn gcx+r) = L-1 titrrnu |= - 2- 1;1,6-1 llL), Lr-L) -1 ,
(ttn 39)=-s IrA:. qrftx))" -5 )
loi{r ftx: = |
'1
filtna',it qrn f Ix+st " xl- x'+Lx #r,tnu X=1 t:[n fcb),1_1+z=
1r,
r
[n21 T(x) = L tfio I.
u

-5

J

ry

-

'

b

d:rlir gcftxrt- -s otrrlrinuq""i x:6
[oir txel l rg,frcxt+5 =o J / A
dtiJjrdo n, rrfi: fl, f;tu-r irBnuu + I

dil,i s{u nm l'r] uqil

fr

,'. do rr" -2n

4a

qin

2L1
2x-s

LX-+7-1A _ 2(Ii1)-10

)= -:-=X"+

Xt+

1

{tn

l-=

rfixir y

t

e

X,Y)

-'1 ,d,
e 1 bn n

1x

I

X"+

1

Lt'- z I
X'+1 J

lv=

.{

fior[]B

L

1o

-

x'+

1O
_-=-

X'+

1

lfiuir

x,Y e

ri"ilfio

t-l
1

1

I
€l

*

1 0 ?rt dr il Xl+ 1 al oir
16i '+1 = l)?-)s,10 ---+ L=or1,4,9 ----' f,: o,t1,tZ. )13
vrio xL+1: -'l ,-L,-5,-10 ----n x'=-zr-3,-1,-11 ---+ liflrirx'fru'r]uiruluflll
10
cir X=o '--) ) = z- O+1 -- 2-- 1a - -Y ti{lrlr'r Dr = 1o,1,-1, L,-L,t,^3}
'ilwtnulu n1'reJi

1

gir X=!1

----.

):
'

fli )(=12--+ ):
,

f,r
@

n.)

X=

jj--+ t = Z- rc = t-1 .
1+1

rcrsaal [rd:

-,r

otur+

coso

1

drrJ

riuderuu

cas!. + co5 3tr
b57

* 9

-

*

<oos?.u

lnuoernnrrrl
ve

,'. 10 n, gJ6-l

lruuou

,.o

sinacosts- CosAsinB

----*

sin

rrd:

1,. 6ttn

'" (H

f;

cos]{ cosf,

sr-S =
sin I
1

'ilS {
f,od
"0, 3
sin

dtrl{rio n fin

"

L

:inIIcot{-cosf

c sin ti-i51
cos?! c ei6(i-?)

cosl.I

x

3

tanP tan* - sinH sin9f,
1b
B cusry
1bn ;G_
= six ({-e )

t-.

;

firrnerir

r

ilnxrTn a frt
I

cosl +cc,slI = -1 -cos1 = l-(-1)=
-5
7
5
L -

fl.)

R.

++1

cost *cos f + cosr =

/o{

= {_q, _l .,o,x}
1; Dr-Br " -t,L,-L,3)

2_-|0 = 2-5 = -3
1+1
2__ 10 = L_?_ _- o

D

{(

sin
cosuc

{

({

H)

da t,

=

sln (a-B)

_ 3T

zl

o,in
FJN

(i "#)

1)

(2--

c05 15

-

c0:-1:"
cos

oiolfrqr:n*l,lt !os'ts" = Z_fr

G ) cCI515o

sintto'.cos

15"

coeo. sin(lci- e)

rE"t

1so

_ tin 15' .
co9

raislr.

cc,g 150

tan

r

15'

1E"

tane=

t tnR - tang
t + tana trn B

tancA-B),
,'_ g
,3

l::i:_;,'j.,)

(3-Gl'- q-6J3+3

E_ JT

s+il

=

t+E

t + tantE't anld

H

= Z-fi
.'- 1,o n" nn

1-3

3

,1

t-)

Coslcr'+

sin$" =

oos2o"

oiosfieumii sin +ri = co,szd * costd

+a1oIo

rir ros {:floRrilouf rfio O *rrn?u
cc.rsto' > oostc, --+ Ccrslo'- custd < o

ctnntrhlrrXuir

, qJri

tr,or sin +r)' >

-,

O

s

in +o'

r'

@o

c

r,s Ld

( 0< 6 < ttt")

- fos 10'

.l)

y+

1ld "il,

0J6^l

Vo

fld$ A = 0o cot d rarnilulo5 rilrlt*.ferdhir.turil hrralu A 1n1

+)

,'

dild A=B=3d

-

! *i

rin2-R+ LorLb = sin 6o'+ cos od =

=

.'. $0 n. ,J6-l

ry

- zsih(A -Bl crsrA+b) . ?-5in f f d-$l cos (irj+:rjt = Zsindcc,s6rj
a&*it :inzA + cosLh / zsin rA-B) cos tA + Dl &rrair n, B1ar1
drtl{o?r

1;

I
Jrr

------r 5thA

9= ?rccos I

---+

J5

Tordl,.i
1A1 cot

2rcsec

([

X

.

Cos

Jtr

cOS

A

4
=

.l

-----+ >[nD

E
5

=

----+

Jf

zgl

-

tantR_*r_ lann_tanB
r+tan+fins

i+l

I

Ccrs

-4
- qd : --2
I

=_

r

:_

ten tA- zB) =

-

x

tan tA- b) tan g
2t
1+q

9z

-

=o

. I

- tln Itn-s) - B

bans

_

tg

q-1
1

1

Cosqd

sinqd

+

,-qQ)
d:r-liod oro.,

tanE "

?-B

)t

(A -28)

tan rA-o)

J

8

l

2

sinro" Sin(A-lB)

* s in LA -z{b)
L_

rl

fr16-l

"o!
cosrqo"+(A-21)l
= sin Lto+ (A-28)l t I:l::'.l: :l;ffi;:;:lll:
ninl;'c

+z

tanA=

s

+

G

= A-

- zor.ros

cosro" cos r n-

.

tr
t

=

",1

trcs,n

+ Xrcsec x )

B

I

=

,,'. do

x
il

mou 1 x

A= rrcsin

r tor(j) . cr

l3

- lc _ /13tx
-

!
12

13

V{)8)= n

I

ut16'roi","uolns'.r+l xt+ 1'= 25

@

d

t

---+

tr,

qfl fr 6-l::rair nat^ldo (+, - 3) 1t61". ( - *,

-v

l=
I
I

+

(u,-,

-+,-3)

(4)-

t-dd

rrJiofl
,l "
LUI

zx) 3(+-

o ,2x
JJ'1-

3.3"
:

3A

tt ou ora

+

3A2+

qLi--x ) = z4T

3t

E1n

I

----+

X= 1f

?'

--+ Xt+ +yt* z+y

b'

+ zcr = 6

orol L x
(l+2x)

dtrl

= 15-(-31-= 1b

-3)

x'*
16i 1u+tY+s1' = I

38r = A

irft1,6

3

-z

Inu urf,unu?trhj rrn u'louosn 6untrils

rrnlniilridoqtruunuion qJfr F Ix,-:1 .L[01 f oi3r.ru
rXuorl I+2Is=o --+x= -zJZ 6i F<-z|r,-a)
qrnn:rr{ lsi c = Lfi , 3 = {, ---+ b'" :'- t2 = 15- 17= 4
-Jd
-Z
r{ oa
X
lc.rrlutjnal (0, - 3 t --* film:tfr fro r- * (Y+31 =1

-2Ja
I

-fr

al

'

L

T + Y +6Y -Y = 0
2t'L
v - _a --f )(-' t6-)
l-

t -,

fo ,25i+ 6Y-'l = o

Y

iIA:

8t

+
6l

=

A

u

1

,flor"ifdsrifi

L't-*

A

oAL- zz+A *il = o
()A - 1)(A - Et) = o -r

L++

=

3'*

Bl =

tl

I

=)
J

=

+ x, -1

1; r'^.3-',3u

L4+

A

I

)L

d,

l^u11 t-;,2.} c (-t,+)

2?-+

I

10

11nn

x

r io no

tdj A

=

det

irfl: dettrnl=

r*l R-'

chdettnt

)
,et

CI

cf

il,dt n n

n,) qln adjn= dst(A)A-l

take dtl rl,rolirqloi de,ttadinr = deiIdeltnrn-']
dctrftlrtrn.,nrfi - ,_-__-i = tde,ttnll?clettn-'l = (det rRr)'
lJ,

tl.rr

)

delorlfi

lxn: dettrr# o +

q1n

A'=

teke

rn

c rUu
0

n'rnrn

I

-q

-

cTuor ta mr

6

n'f

y<

1rs n. iJfl

?-A
!

det

v

det tL n)

{Y

ril6txl1l tfrl

tor dei R u1r

= Lt de+tA)

1/

,<

l,fi

fl4061

r deI tnr

=

10 1. o,lfli

8

dr,lioil r',ru + x
'fl 1 q {'r 3r xJ fl 0 { il={ bx ru 1 n u n', r

trt/c$

ailn1r10qlnfln0

$x+11 >rb

---+

LX'l1to

--1'

0()-.X

-t

Y
Y

>t -Lx

noruro"toi

e

el o{ or r ""v

i t-l r'k uel

a

I

Atf , 9rr,'b(tct,to),

J

>,'

Lx'

10
i6'l

X,) >tA [r^? 1<X

A

B

y( ... r,rnr'lfinril'

rr

>t

... trlut{un:}l

D

d,.

nllus P:

Nnfrl

tL 6r/
1 '3
(10,

16rA
,

lt

J

I

fito1]

'L

3(lo)+ +(lo) .'10

mih
max

P.3(S)++(o).15

?.9(z't#4(o)-9

10

9r,9) dflfr

"
dlU11"uo1.[

P

(5) o)
(3,0)
t€!

(

I = a(!)++(9,)' r

10 )

vnTil1 P alrnAnno

3k + SY

'u0

F il nr drrAfi
I

*

nqn
rr,o1 I- ) f 3

a1

10 1. hrl

l]n

U +V

-

,0
A

Y

q

il

[r'r u+v = w
.
!
!
dot il nr {ot'irlrrotAHnii

v.raj

u.h,l
,JJIJ

ilTlhnl

+ '

=

^,1

,

ur,'H = 8

v -hl

V'

Y'',1

-Z

"

J2

ll,fl: T'W

lhl

=

sQ

lNt

---+ lN.l
d r

J4

V.

-)JJJJ

q';!114m1 X-y=

=l;

I

Tt1}.lil nU
1

lXll)l

€

v

ver

y

8-

L
I

2

{l

JJI:

n = lvltNt

otrlr

-L

,J

CC'S Q

cll

crrs

(lr -arcaiht )
js

. tittGl (- cos tarcctis-r ))
G
= tY l(iu.r(- * /) -__f li I = jz
r 13

_L

J

,

tl fixilei'uor Iin1fi0511n1

fr i 1

IrA:n [fi An0un0

A?-

lhl-= 6
el

'
n"-[rt

JJ

q ?1

m = til,rrilrcc,i(aresin*)
8 = rd,rtfi)eos(Arccosg )
,-.
J
g = ril.rtJT,(E) J5
rdr=

'1

JJ

g+t-Z) "
JZ

rnfi 1qn+r ir',rrr* nll;r

--rLJri

til. t-+

1.{}+

ti l' = *'+

[.lL

lt

=

1ts

dril{oioror + x

*

Noto

Al'csin)t

:

=

t lc cos

X

e

gin ( 0rcsin
cos(1I- 0)

@

11
_+ _
A+c b+c

qrn

( -l-<xs l)
(-l-<x< r)

tFcsinJI-x'

0Fccos

|

- xa

X):X )
: -c059

X) 3 x
sin [n-6) . sine

cos ( arccos
)

(-l<x<t,

d+b+c

I (a+b+cte= a'+b'+ct+ z(eb+bc+ac)
btc + a+c
(a+c)tb+c) t+b+ C
Ltt+btc) + cl ta+b+t) = 3(i+c.)(b+c)
.z
(E+b+c)'+ c (atb+c) - 3(ab+ ac+ bctcz)
1

?'+ bo+cr + zab+ 2ac+ zbc

+ ac+ bcr

a'+b'+zcz+ zab+ *c

=3cx+

ct = lt+bt- ab
-o
jr c'= ?',+ b'- zeb cosc
11nn{no31n+ifr
rur O-O', a- -tb*zabcosd
abtt - 2cosd, ) = o
*.dr

,i,u,

etn

{Jfr

a,
1

nL

6trl ioil
.{r

b

filufr',r-rtsl frruly*ar?

-2cos

nsu

3

cz

t+o

d +-g ----' cos d =

1

= 3tbt sic t 3bc + acz

oab*,+ac

-o
[[1t1,50 l-t

c=

60

slnC= sinod

.E
L

.

R,rnt ir rtndrnrr

1t

fitnol[rn16 0=b=

C=I

3*c
-+-= b+c +8+b+c I + 1=1 dlnr:rilut'rt
1+l=
qJd 1+1 1+1 =31* ?.r1
''*A
z'z 3
,iura:rluneruil A rgc itl" a frruunr lunruunnilr.r = 6d
{'111
oilrrlu sinA = sihB : sind = sin6d = g

zX,

.l

q1n 7-gZ+$= 0

lfr
i;

lzrl'=

=

lzn r"

,--+

rz,l'+ r2,r'

3t

Z

2( l)

= 9*r ++

z

(1r)'* ( J;
1

=

_ 3t

32- +U)(+J

)

gtfii

J_Y
Z

2

I la+btl.la-bil. JEu-"

+

4*4 =$

nrrlifrir 6untt o t('* bx * Q= O t{nUanntOrOU " - ! tun flrB ntaror = !
a'a
a
q1n z'-szt4.o lrizuo uln n 'lr1ou -- 7.+ 7, = -!]= 3 , naqorntfl0ll = zlLz

trn

1

oiluur 1*1 - 7t+zz
21
zrz
z,
(lz,lL+ tz,t,

lsi

1

+

i. L t- (n1i1 =

ror +x

drr]{ofl

L

'1

t

o

3n= sin(nn-I.)-cosnr = (sin

11n

)=+

3

=

t

=

nnrf-

- c05n1[

cosnrs

- ZC05nT

=

;h= l)2,.

Notc: Cos(2,nt-O)= cos g Sirulu fr =r,L,r,...
Yv
In
bn= Lco5(znr-{) EcosI = t(1)=g , =r'2''
3
drraiunn n= 1,L,3,
bxru 'ir bn= r
r'r

=

..

lr

!J6i

- 2 CCrS lI _ -21-1) -3

=

b,

33

L

/ 3r

(u.i

/

l br/

L

-jf

i

/-Zcoslnfs/

=

titolrtn 2r
r""loo ?u=

-2CosZT

)

I

z , Io
t

3F

=

1.r$

t:f

olrnnhJfirLb

I

)

-

) = (i)
z3

bn

*(Z )" (:).
3

z
2

2

3

-,rt'
3 I - [3/

fi rr otuu', siu

n

/
darjlo i r t.- 3n

r.,ro

t -z(-r)i

3

r_fu]

( u )=

=

1

-L

1l,

-

d

drillou6'10u 3

li'rr n?urr fir};

{,16i l,, = * (

6o',r',

=)

2

r=

{l

!z

x

r

i(ruiru ullu

oirnourarirrarl r

"

(:l-

tril

r,^tJ;

a, =

)

1,1, er rilu nrflguflordarnrt f rx I = o uunn0 I- 3, X-A x-lr
r
r1l" ui rrjr'" oil r { tx l .q rloi Irrr = (I- + )(t-r)(x- ar)
1A { rx r = x}- z6,,t'+ bx - zru = (x - +)(x- a)tx- ?r)
x'- zsx'+bx -ztt = (x'- r, - + n 1'l(I-art
xt^ t-txr+b x - zrg = x3- lx'- ll'* & - arx'+ x'rx +{x -t

tl61

-

<J.Sr

4

)

n

zuu

a

X3- zbx'* bx

-21r,

=

xu- (
^

*

gr+

tr ) xz+ ( 1j* arr + a')

x

-a

fi uufiu.J,tfini {''rna:mr r 11fr

x>
,.. x

7b

, b

. I + !r + ef
L"L

= 3+.a'k+
Y

> z1L = a3 +

16i f tx)
t'1fi
t't1)

2_6

=

=
=

dtrl{oE *o,r

LUz

a'

X=

6+ |+ 6r

a(i+r)

l*r = lj'
r
3

6

x3- ztxt+ lgrrx

-

axl- szx r 156
3- EL+ 156

10'7

--

L*

=

L1L

--+ F=3

L6
3
=Cl
:5

+
6

b2t3) +

(j*r*

'(:)

=

r)
( l1)(13)

,

15b

a

(9

^el,-(

{cn,"riunru,orirfir6ol

Lqnilrirrar+n'fi

1orrfi fco:=1

fiilfr {txl = axt+ bx + c rror {tor = 1
q1n {tx+t)= ftx-r)+xt1

1'-

0ttl)+

btol+c ---+ c--

1

btx+ll+ - a(x-1)'+btx-r)"ttx+t
rItxtri- tx-rit + bitxtl) -LX-1)] ' x+1
2txztzx+1 - xt+zx -1) + btxtl^xt1) ' X+1

Id

a(xt1)zt

4tX+

i;

---r

I-b

= x+1 ----+

J'{rnd* " J' (lr'*
-L-z+L

1x+t)

,fiorXr,ril,7n-i4lrrlnsrtr'tdi s?=1r zb'-t --+

dx

=

l=1, b=l
L
+

[frr'* *xix]', = (*rtt*+r)-(t; +1-z).i* frz=3

6rrJ{odo'rsil 1X
lr+ x-

li rn
xrrt

J-Xtt

zx'

lir

=

-

l(1-xlt1+zxll

r_i1t I-x*

2

_

lln., lt-xl

=

x,1+

Z

Jl*

I t+zxl

-z

.lt-xl .I-1 faoxz.l
. ll+zxl s t*2X ,da

X

rr

-L

-:-r = xrl+()t-1)(2x+{)(ll+3+2)
lirn
x+1t
(x +3 - + )
(Jxt}-zltJ-xt:+z)
.l{ur{urrarharr
lirn (2X+tttfx+l +Z) " (ltt)+1)(It+l +z) " ())(tf ) = 17
X-rtt
ne+cJ-xtg+L)

, ,t J

6tr.lrrou eiotr

3X

lrun',r1'l0flantfrtdosnnh,ioaifiu flcs) = 6x6 = 3r

l*} = I 1frit E = lt+,+ ),(ttL),tb,a)i (""1*l=1*1-l+1 =lr
'' r'4-7-1-1''7-L'
eb z

frrrr,fr:..dssrrfix{snniorril

loi htEl= o

----+

PcEt,

xY

X

Y

I

3

L

+

+

6

q

tg

+

'7

11,

)

X2

10

L9

3o

55

101

*t

@

-O :

1o.l

nc

[l'n%nl h,5r 1,t= 15, 2y = 3o, ZX2=55, Zr) = 1o1

3a = 15fi+5C

-O
=
-O
10 = *51"fl + 15c
-O

10'1

5O

15

Z)= mZx+

ZxY = m 7x'+ cZx

b 6-)

5

+*

dxnuritlrl ) = rflxtL
dzunit,nfi

3

1

dtd{oanot

lL

Lc6

['5

Z

nt5

g

1

3l
lb

nrEl

rir $ xl

Enn+ 15C

-10 -- ssrq - +5m
1'1 = 1otfl

rn = 1.'J
ttnunl fl-l " 1,f m 0 '. bo = L5'5 + 5c --+ 9L= *'5 -+
loinalnradilrJdo y = 1,'lX.+ o.q
Iuual ffl+[= 1,]*0.9 = L.b ,',"]o nqn
frt x" 15' Y' 1,'1(15)+ 0'n : ?'5'5t0'q'1-b'+
,

C= 01

dt

,Y

Y

eirru,rnnfi{

n

![611

1,

fitr1doBorgu 1

X,

1J0

fl nn
'v

n

)

drnr:nfiauLiir Mo-

I-

larat
61,

x

fxrfrlilrinfrrr?rnurlfrorurr*u,'r.lu

qtniuonir x ilosnir M, sadounrtot s
r

X= z5

ncr

x-r

)( = 25

!r

v

A=0.5-o.151 = O.341

)

rrqn

n1?

rr*

s6

dnB

bo c:Jfrir

<

-1 =

fitR=0,3a1 ,Z=1

5-

5+

rr,qr

11 =-2 =l

--z
.S

)

dr

rtrj ir n r ulu

54s

Mo=

X

.'" ?o

n

f,d

nn
IJ

6 n'r: trd:el1*
s

60

x

b

a

G

bo

6o

etY

iul{?110 n. llfl"

1,

@

I

b

3

2

a

7

z

U

1

d

3

C

Z

I

b

x

ulxlllu[8.i
o, 3 tra'.2,

..,')0

= o,1

frrd{oioror I x

nnflgi

-J,

-'t

1

c

L d

J

2

o

1

,i

L

o
1

J

1

fi,lfiu,a, I
:i *
-l'1 ,
0'tr:tln [fl fl ouu no
Jt

6

dt,t

b

1

L

|1ru

2

',l

01

I{

S1

',l

c

Z

4

0

1

J

cl 6l

1]nn:$n

d,

v

br

d

,'

b

ulf;r

c<

d

.'" 1J0 'lt, nn

d. rtlr c<d
a+t = c+d

.'" 'uo n, nn

1

n1

1

[1' ]+?

1

n1 a >

-ri

{1n n[6]bn

1

r'.

r4
qlnnl

rrhr

bu)+?

st_

lli

1.r? 1

d,

2 nr6I+ iuu?'t

drrl{oflmor

",x

n1

t0

?<d

z

41n ntr).tT

1

* b"C =O
' frr 3=3
) frr l=o + [=6=J

1

2

q!flotrilurA"t}

0 uto s tnlhu

o

L

dtadr

nlo d

I

a!,d

1

o, b, c

tnnuX

b<

n.

0.J0^t

v

v

.".lJ0

$.

nn

r
d=3 +

d=o

.la

nrorh

I

-lnrdfiz

lJ

nn
I

1i^ n(AnB) = x

,

frs X -> loo1 1Jo3A fis 5x -? p11n1 = EX
> 2s'/. 1J03 a 6o x I 1oo7" rrol g ''no +x - h(D)= 4x
t-o"l ltos n

11n n((A-B)U(0-A)) = 112Intnl- nrAnBl] + [ n(B) - n(AnB)] =

117

- X) + [ +x - x ) :- 112
= 112- --t X = lt
hthU0). ntA) + n(6) -n(Anb) = 5X+tX- X = 8X = $(1b) =
( 5x
YIX

6lt}{l+

oiorinsuit
"r

A

.

i n+s4zlAs
l

({r;*JJ)*(Jrx+r+
zGxtr

:

1,"'i,

1"
bfri

A=

JTI = 1t

3X+1=25

5

I

x"{*s 1; A'

1*

AuE

trclan

A" {g}

X=E

)1gx+s ---r 'l-A', zxl-(, x r10
Iz)t'-6x+10) +1+L Jr-rx,r = Ls
nin^1L.(t
L-AL+zh -L+ = O
(A+A)(A-3) =O
-r-) A= 3

z = lx'-3x*

=

5

I = xt-3x+5 +

rirriu

1q

1+-3-'-1 ='lo

Jaz'tr

lr; A.

*

ln*G

=

+z.lt3xi1)tt) + Jrnx+1)+(e)+zJtlx+zltq) =

(1)

Jtu+1)+

1ZE

i'- llrr 4 'ct

. { s,4, - 1 J arnurn6alr?nr"r]u u

l = ,1 -)

1,; *ctan{=o -

tanA

I

'

+ " Qr-1
-rJ

X

* tan (Xr))

3

=

r

tans-- 'l
1

rioliir rec'o= 1+tan'o
1rrnl = secz(zA+ts)
=

1

1

- tanxtany

+b anLrzR+0)
tanzA

tan zn + tan

-(

.l-tanzAtan
3* { 12

+Yl

1+

,

12

t+

(f,xfl)
1

=

1

1- (i)t+),}
1+

z

=2 x

z(j )

tanR

- tan'a

=

l-

(rr)'

a

=_
+

-a<asinSl

nrruialilr+{oildo
trA

;

n

x'*

A-

C,os'0

Y' <
-:in+B

=
=
.

Bstno+40050

CoS

-+ - 1 < C0Sl0 -< 1 rirlrnfin

Zb

txizx - tt +

x logr-, (x'-t zx

(ir'-x)tlo9r(x1+Lx-1) +

-

1

-x'

Lx

)

(})t, - L) (log, 4tx1zr-u)

q6^r C th,

z)

L o-r

l4xo

oqrrulfruerm y

s

A
"

=

ln

rln:

nsrrarnloidaLnrt 'lX -3Y +

21 .

Bt-z,s)
{7

}t,n. AA0r .

CD

[o hB
! ng.co

*

d.= lAa+Bb+cl

'Ax+BY*Cco
- I rt-r) - 3(3) +21 |
i+1+ q

.

J

(I,.Il ) t

Btxr ry.l

bc =

r

inuh

Rr

J;ffi.

2:
z

) il def 1.on',,virfiri61frrArrrur

axs firu?otn . ri.lld
t,srar dei ",ir., ,,irrr..,* z l:1frflufi n
-5 -L

w,n.

A

h0c

=

J-st

-z s rl

1

-2s+1+ - L +35 ttS

1+, 5

z
-1

a

1

1

1

21

t-21s7'*l5lJl' = J;r

. j,'tr',(ffi)=

Sol z

ldtur,zuninir

O

)

,',.(e't'
n)'-'

.

AB:

" 6-c
(-s -h)'+ (-z+hr+)' = j t-r-hl"+ [r+h++7'
tr+hr'* th.zr' = (N D'+ (h+t)'

urArnr: tkurrr il u'.tr*1ri A ( -s,- z) tr'" B t-t,s)

[6-]

)

'+roh+zs
= '+1$h+rr
rh : - g6 -+ h' -t ) k= -t-.])-t =3
loirn c r -r,l)

A(-5,-1)

A(-5)-2-)

- [t o I -t]
', Zi
Z

B = t r', (rrl', (-9.)' = I n,:r,T
J
rntlnfiufin'lu B = 4+? = to.sx

t

AC=
lv

6

I . -!
Lz

X=

-x-4

B(-Z,s)

{-r,l

fX- 5 = g
(LX - 1 )(Zx r 5) ,

A(X', Y, )

kl

1

4XL+

slr* r.l,,frrt 0i,1, ui,?i,,il u

-h-+l

Sotr)

Iogr 4(x1rx-1) = O
4(XL+ t-x-1) =

:e

*rJ6 c(h,-h-+)

C

=

z---r rrnr*nrh;s lo3 tfr llt-r)
* =X ,
ucrrair lo3 , o"

'1 v

t[o1rt]'+r.x-,r) + 1o9.4) = o

6'urrm,1l,*l-rl lfi

x

1

,,u',

zr

e+b. t

3sip10++cosb -<fi3+4;
Rr sJlndot
ssino + Aooso < 5

z
)x'ogr(xiz)-i) - x log, (x'+ zx-t) zx-x
log,tx'+r-x-1)(ir'-r) r z(lx'- x) :0

1,*-

b=1

' -l?++'<
- s

[ogr,

- sirlo I

(oor'o 1 si nz o ) ( cos'o
(lttcosZo)

5

x'

<a tta: -b*bco:S<b

-r3u

-'lit,^o

L1) - 1a.5
X

-+

I

nt

-,i I t nufiurr

",ri,u^

mI 1

'.r1n1flfl061 A (- 3, z

B(a,b)

%11.b I

rnu

X

q

*fr rfl r',[u a

"',

olrffio.t

I qfl f ciorUUlUr r-oruari*rit qat n

l; F(x,z) lrm F otruuitxortr 4lt-3y+14=0
iinunt 4X- 3(t)+1T=o
Y'z
4X. -B -------, l. -L ----+ F(-2,2)
x
6arnr:nurlualfi0 ty - hl'= 4c (x * b) I xrrror:rnr
Irnuritqnuofri A(-l,z) ---+ h. -1, k=2
rr'truro^rt C = r:tr:urt{flh0olfi!q6-lI = -L-(-3tr=
4 tX +3 ) llnilhtilccrolnrilAe.rnu 4x-3Y +,14 = o --+ y = 3) - t4
1

(y-zl

e!7

6untens

=

+
nr'luf,amrrrrrluarbfiourqfloinr
rilo )=1
|= -rn qneinfis,-1,,,
()-2)z'+(!J:11 *''1
4t

ilnunt | = 3l:l-1
+

)'-+Y++ L

,fio

3Y-1++1L

(Y-1)()-b)

O

=0

n r y dolntu 4rut.qfrlfl61[6] n ororrr
r
0
1
tr
r
-+
n1 y [rJnnurarnr x lufialnuhlilhuAr vrJs
fi

@

atnrlduorrln

'lY,

[fl 1i[1in]

il= [ ::';"]
JF

,

.

Xnlntnvl

r[fr

J

-l

AF

r1n is1tatcan)= 4
)uunderld
ro d.ts-') ='r tl'
dr*r clet
det

tcl

=

a>o

A(*3,2) F[-2,t) nf,r 8t1,6)
* Lorfr,iorla''ooufru
A'F = l-?-(-3)l = l1l
L 2_- z ) - Lol

iEo Icl

ctl'v

1.,

ror*Blni

Y = 1,6

v.

roolarHo (1,6)

qrnknduonilq6rrio D(a,b)
lrite'' Dfro B(1)6)

')-

) -'1)+t =

1

)=6*x=

l;] lil

FB=

il

det tBt)

=

det cD'r)=

+

ti]

=

=
detr

(1)(i)r(o)(+)--

3

gl

I

EGr

u1 dettn; = o+6+o +1-t = 2o
1^j ds{tctRn = dslcclde,ttRldeltcl= (t)(20)(4)= 3zo*
Z'n

=L+4+6+.. +Zn 2(,1 +L+3+.- {h) = 2[lInr:tl = n'+n
Lz)
h1fr*l)(zpa11 , n(nrt) _
lui bn = f?n = Z tnttnl = Zn'r Zn
-- z
q
h+1
t,
e 4-l=
l:+-+
lim(itlt
; lirn Lb, br " bnJ 6ao6 i=r bn' =tim (i,=r f:r- /t
hJoo
1!flll!l!
11n

ah

-r

=

613'

I

n(n+

2)

,1(1
-

,

n

_1)

n+t/

t

osfl
=

=

Z

nin+1 )tn+z)
2,

h

3-rl
+ nrn+zt i J

!
lirn l./'3 * 3 + 3.5
n_d I 1-3 2-+
-+

i Ig l(i-u.(1 -x)-' (-).',)"(il!.#I*(-X*#)]

a r,
nJil
-a 2

f,*1,

itl

o-o)

=

n(h+l)

g

ti",.(i tn+L) )/
'

.-^ i-r

i Zn=
i=i

_1
n+1

_ 1l

n+zJ

1
+

=

2-.2-5

*

'4',t+rur1r46%,q:Afrrurh*ns,iwftiuog

, heu fruAr"f:r u'1,

"i'1":,":ntn
i
1nuinuftlfiu,urfi e [< nr",Aruiunrnrnfio rilufiouriu t t"darr]l"3r-'']ufir )

( 1rn )

:

'r lz t lz,iofiunit"uurnlor z rrrz,tlfirtn I , R.l'- '{]rf
etllqnic'lfr zIa+bi +r= Ia+br++l
z l(a+tl+bi I = lta++l+!il
LBe-r
t-Rcr

!)A-l1

lm

fi

2 .lTa*

b'

1)'*

=i

q1n Sn

=

1ri

=

Sr,

0,,

-Q

q1n

tln 2= e-bi

lt + b'

vl+

atr fu+

16

+ b'

b 6-

r?l=

m(+)'
Ia b,

:

1

fi4il?n

=

Lx

i

=Bgs
l

20

G

ununr

da

hl*l,tlnnn0 5ro', 205+505 ='l1o

tza,+(n-1)A)
t'

=20,

5zo

1,fl

= T (zalrtqJ)= tto
23, +

-O

tqd- qd . Y1-41
=

xt+

q",[fil+t

2n,+eJ, = 41
lii Sss

(3++l'+bt {

aro

frza.uqd)

@-o,

+F-i- ') ,nirxs dor firf,o 1fl1i

cJ+

i.r^il?n rc urid"Ll

t,

uAilln to xl*rrln = S,o = LO
i-20!
t- 305 ------r
#
1,,

= E+bi

lnr

+(ta+t)2+ b') =
4(il+21+r)+4b2
4?2+&+ o + 4b'
a a'+ sbz = 1z
22+ bl . 4

ar

6i1h; z

tod = 3o

----+

J!tta,+s$d) = Xil++

5+(3)) :

d=g

----+

f

rr+

19d = 'rl

-@

t'T'r+ntd'rarA

ol0r=

1+

4 tbt-) = 55(BB) = 4t4o
x

f fin,,d,-,6nflutiniilnrfiuzfix=t dilfildli1 ftu=z u^: fltl=o

+3 ---+ ftxl'9tx) - 9-X+3 6?.1 frxrgixl* f'tr)g(x) . L
i1n 1" tx) . 2- ------+ g'tx I = 2x + C -@t
rrnun"l f rtt,L,+'(1)=o 1u O
fttt g'ut r l'r1) g(1 ) = L
q1n (f.gttxl =

Zx

O

-o

(2)9'(1)

1ri 9'tx)- L/,-1

+ g$tl
------'

=

|

----+

}'rt)=

g(x) = x2-x+D

qrn

1;
1

@ tlTt% x.
g'rn , z+ c
1 .2-1C -*
1

-o

f,ltgcrl. t-+3
2g(1) = 5
3(1) - 2.5
lrnunrt 9(1)=S'lu O : 3c1) " -+D =L'5 '-'-' D'1's
rl"L
oi Jtxl= x--x+2.5
.5
I tn
trl nr rh r
qrn O

l,[Tlt,l

X=1

= (x - L)'- i+t.s

=

(x _ o,s )" +

2.zS

C = -1

nr

r

,'t1J')

a

e cr

or

r{

or o

oi,'ilr, nrr1116cr1a,rin6fro

it

fi

so

?-

Ls

aon

N

10. s,

z.zo)

't"

x1s

Lu

,t,

t1n

[cxt+

t;

P

X'=

t-3

= 3 (r')'+ z+(xz) + +D
= 3(t-a)'+ z+(t-3)+40 = 3t'- lgttzr+ l+t*'12++o

a)

(t r
P ( t)
I crl

= 3t'+ tt - s

= 'o
['F.rtrd.t = r* (stz+rt-srdt = [t'+st' - tt]', = x3+:Xt-sX
l,rn Jprr) Jrt ) = J r,r,lJiu = J (tr+1?.-5)- (r. +1L-1;t)
11 - lcr = J? = J*,
x)L

111

c)

Irt1

y'

=

f 'crl =

!e

Ctotx utnai otnl
"'1

{rn

ahx+ zh

li m
h+

Ptx+h+z) + Prh+z)

cr

o

P

t

- Prx+z) + Pch+zr - Ptzl
li, tJX+L)

h+x+zl

-

X+z)

h-ro

Pcx+z)

+

= 3X+2

lhil:lallr

lor h sjroa,r',ra-,edr.A'rr

h-ro

lirn Bxrz)
I,Jt

- f(x+zt -?ctl

ht,?x+zl

lim
h-+

li, Itr*ht - frxr
h+o

n

L

'hlrrnr+11r

P'rx+z) + P'tzl
Ltn% x

" 0 t" @ '.

Prh+rr

lirn
h+

-?rtt

Itirn,,,',u lim

)

=1

h-ao

h

tr

=t

P'(x+z) r- P'[t )

P'(L) + ?rt2-t = 3(t])+L

---+

"

-o

3x+z

L

LP'r.Lt =

----+

P,(L)

=

O trrilF'(D,1 '" ?'(X+L)+1 = 3X+Z ----+ P'cx+t) .3X11
1a
Ila A = I+z 1 , A-L ". ?' [A) = 3(A-z)+ 1
3A-5
1, PtAt
tcl
= J P',nldn = I(3A-s)dA = 2gL- sR+C
: Piol ,2r*ct)L=E(ol+C =1 ----+ C =
a1n Prol =l
.LL
lAt Prtzt = 2(1L)L* j(1r-)+1 = it1+$) - 60+1 = 216 -5q = 1By
*
41n

=

1

'" X+ZY=U

L1

fn4

Lr : Y = firX+C

r riu L1
16i rYl, ff, = -

: -L
rirul fi
{

-t

(l *1

6-X

-!x+z

z

(0, 1)

urrlo,sio'r L,, riu

ufl;

t,

Y1= )z * --IXt3.
I

1

fn' = L
Lr, )= zx+c
qoiiru ( c', 1)
I = Lt0)+C
C= I
Lr, ). zx+1

i.^.,

Lr, 7=2Xt1

(-l)r, = -,

la

)

rr,m.rx=1,

r! Et/
s, 6

hn.?nfrs2
XL

Lrnr+ nr

6
L1

I= -lx+r

).

2x+

'2
1

-- r= t

,)z.yr=

=l *

E

llho**

a = I to.t l(1 +2. u)
- (O.+)(3.6) = 1,$t

lllttrn--

n.n -rlrrior

ba'l

= j ta-o.t)(?.6)
: (?.6)(2.6); t,.'l!

1,+++ 6,-16

, f,,,X

1ln 0= {ra,bt 6AxAl o< b-1('1 ! riufio B rilul"um$ogFtdudu
t,b e i1,2,t,...,k] 1o u n n Islr.i u fi orrl'u ocb-r-.1
frcr:odt o<b-t-<J ------+ cr < b- a n b-a <-7

t-

( a,br

lSltr

n

der

>1

c,

, "r)

blrr+? 1n 1

?

L

#,0=k

*

Joi

b7

k

n

b-<']+a
rilu{r rJuil nr b froalrr

br,x'ri krutndn1uA trXl

A

r'1,

flnlu ) = k-1 ,
a = k-2
a = k-3 .,
4
d = k-+
d = k-5.,
a = k-6,
. k-y

,

,

d

r

=k

b

=

k-t,

k

.{

k-2, k-t,lr
b " k-:, k-2,k-t,k

:lnl'nrn

b

-- L$

b

=

b
b

= h-b,

k-5,k-*, k-r, k-2, k-t,

b

k-:., k-b,k-5,k-+,

=

a

b

k-r, k-r,

B

sl

k-a, k-2,

h-b, k-5,

k

k-i

b
I

b

k-+,k-r,k-z I d k- r "do doln'- t
't1

g)

I

FI

{

-llu

t=]) fl 0uou
v

I

b,

dnilfrn r14 qdr+oirr
raf Y,
?-z + tk-tt[.1) " ] 1+

"v

I

J,8,1
2-,3,+r5rb,1)8
3, +,5,

ld)

flo}tou

l

iack-

-9

d

h-"1

1+2+3+++5+btT

= k- +, k-a, k-2, k-t, k
= k-8, k-*, k-), k-2., k-t, k

= h-r'

d

l,ri

b

)

fl,,; s

'l .

In

l1n
q1n

=obr = loporlob+c -O

X

--* k= 106 4

++k-c = loL

r,'ilr X= 231 = 2clo + 30 +
. 1oo(L) + 4O(5) +
1

=cbc . looctlob+t -O
0-6' x-) = (100nnibk+c) - (100c ttlb+tr) = 100(a-c) -(a-c) = 19(?-c)
nr q:Iu x-) : a1(a-c) dnrtrnfn oiorrl 2=9 trA: C.1 ( x-c=t l;?Jrndfi)
[u1,6?1 b ,11*rn'uo:rfll6inlxilt t riu 1 rl^,rx',,,ar1orarIm*rrir,r
L6i s = {ltttqb1,q41,qg1,961,111, q81} rnrln'lug = Y(101)+ (u0+30+,..tro) = 665f4
1

Y

dtt

1'l n

11n

x+z

z(X+z)

,

X+2

)=X----+Y=
3Y = 3(qz) ------) 3Y

( x')
=

.l

,x+z

L.

Y'

_-+

1+LV

xr)+z = 16 ttr,filu,rrunr Y= X
1; X+ x'+ lcxt-11 = 16
L
tz
.5L
2-X+2-X, + X^l
.:X2+2X- 3i
=Q
(3x+'tl)(x-3) = o
1{
ln X = 3 ('." x liuirutulfirlrn)
11n

L

--------f

y= 1+L7

nL

)?=

1+2-Z

1- jtx'-rl

,cxt- r) )

z=

]

:3

Y

ldo'loi

= )=

1v

L'L

L5'l

3
L

16i

7
-l

6^l

x

tx{xg

= -(X-1
z

X)2.

(3)(c

1

= 1 tt - t )
Z

-lL
-l

)(+) = 103 x

A

:

rfl::r

"(rln 'l {r n r:

c)

: druzu nufrli

dd

n

r",l

r

C

n(nUBUC) = 1t

rrnlqnd n(A)= ?, hlb), Y1(c).10, h(Bnc).

11n

6

n(AnBl: 5 , n(A0c)=3

-,

nr0nc) _ n(Anc) + n (nnBnc)

c) = htn)+ n(B) + nrc) - n(An0)
1b - g+10+10-5- 6- 3 + n(An0nc)
ntAn0nC) = 1b-14 =l

n(AUgu

nr.+ff

rtludrir?nfiros dlmrrBut lnifir,+il
e

-1,
LR0nnuuLL3FI1.s1lnflU 6

=

dr.,fl t,rro',

@

Cr.

X --

= o.tq

++ -

=

6

nrr

rlz

Ir A- B)

=x -N

X

=

PtRr

=

(B)= 0,a6+(0.38-X)

0,3o

1

nUffl 6 C<J x
?i

0.56-x lrndi# F(s)= o,3o
r-t

* 2*

3

0.

o. l+

-

Ptnn sl

l[ x

;
h+uunr'rlu a,b,L ca<b<c)
llmirniuon Me = bo = b ,N A= zx = lS=
)
3
rfir-rir 2=CI.r rL61: c=6r t-.' ol.1+ &r = f,ft*fi-- I ) 6.1.r+. Og = flrl+t) 3)

[5

=

qrn

IX -

Gr

+

oo

1ln dd.fr rruqfiiu

+ Qu = 195
G3

-G, =

Qr+

g*

?1

@ @:
{
1,1

loo'r

,).

or_l

l,,=
'

6S

[cr

S

z1g

=0,L

7-

1.1

_

1'5

Z=

65-i,

x' + NrNz

-----r

Gr

- G t -- Ltl

6i =

,L:

-.

11x[o'tqrn

O

-

= W _ tlt x

,= lt
b5-Xr

-|

'l.3X.,.OS

4U+ 30

=

fr)

-b

4550,

+ir=50

Zoo0+ 3O-Y,2 ----n

_L

x

X

x

- t5

-r5

61

85

fi,rJfr n,l,rufit"urfouldl'r]u x

1z

-2+

l,r'-

,.
lL

7= x-x

1.s1

tJll

rouJd c1 fr:t[l+u

x

'

rrn @' er =

5=O,lXt

$,JX1 =

t4otc sol+ r :o )t

c.
)

B5

X.6s

2Qc =
Q3

121+25,+ 2,5$

r otrfior dsl roulai n: rruuEn ilu drmortiru , - 2

'1

0+O:

I ilru = 65;

Na+N2

=

l

o,t^1,t

N4
=

X.

uru

0.2

(g4-6,gtz+ (60-6s)2+(gl-65)1

*

[[h%Fi1111

=

135 -O

33

s = b5- I,

q1n X:,,

Q,r+&. =

tl

uA u t* rA

1

6Ir

135

x4
a

t1 u

Gr-G1

G1

.

r,=x,,

J

fl

fl(x-il'
NJ

-_

----+

1[2
{81

5J|

aonl narr'(u

n:rrlt1d

i= Zfx

n14

)ti

5-7

-?

+0

10-1+

a1

5o

s-11

1"1

36

-

LL

Lo

(I)t+0) + (12)tso) + ( 1't ) (30) + (LDtLo)
+0-t scl + bo + 2_O

ZCr

?-t+

h

l,i ( An
b"l-

.n=

l-

1t

1bb1

u

=

15t1 i

m*l
1+

=

,rll

I

on

a+b+k= 1+14+1). LKX

nt-n-t

nn'

h2.

L

l't+n-

nLn-

1

11,

t511

ll ,

....

1

t

(fl)

(fr Xfi X+;)

9,

b

,

1

n2- nn

-

3

h+

rl"

nt+n-

= 183 -- 13+!
1+
1+

1+

I
t+-!-- n' - nt+n-1

4d6 -

[ln

Lr+60+s1+44

,

dotr

)

nt+h -

n'-rt-

1

r

rrnh n 1 l'l = 2 ,9,$,

= ht+h-1

L

h +h - thXL = A
(l"t+ari( I'l-16) = Q

@

11n

5t2 + rb

+ C

=

1^t.:6 y

41b

r(8a+b ) = 41to - L
aa+b = 416-t
7

<$

tlt0

t {1 n

n1[vl

2,b e Ir,L,... 1t trr'r]uiru:urfiu
416-C e t* dta
'7

,dr
c'10

i [fl0 n

tnr

r

[nrl", +1b-1 =413=51

C=3
,,
,e+ b = 51
) = sg-b
I

#rrlri te+b e/ t+ frtu
J,

1

rln x tiiuiru**1fir" drhi sq-h e 1+
fllrfisn b=3 1; r, 5q:s3. 56-v
-t
x
cilrir* 2'-'1 , b= e, C =3
?+b+c = 'r+3r3 = 10
1;

,do,

8

x

dt- -.

d

"[c tilur']%tLi]01lt

fri'lu

Pat1 ตุลา55 พร้อมเฉลย(2)

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Pat1 ตุลา55 พร้อมเฉลย(2)