Ax 6'1

iET- -

Jt": = ,tz-, Ta,aJ =., [_o,tf . 6) =2.

;olill ^n-2, 4x =!.= ,).

Lal , T) =ro t'u) 4'x. -:: tc ^ I- .- i -o-'t'j-- '- lo ' ,1

a:ln : ao * ,L. ax-\ = ot r t.r) _-- .tix2 = 0+ 2 (q)= -1 .

An = .r l t"r.) an' 'k=t '2

=7 VTa 4x,k=l

= V6. (,a) + rlT ( r)= o.SeJggjSg

Autr,

f-4,t,, 1 = l_o,r]

qI<H

4

?r3. .!Ool = b'mx;

Jrlln: f,'t =2

4x -= -b# -,. Ji . ,t) ::; tr lz

A :a 7o * !,,.'at'\ = TlzX2

^n

An : F, j (**). an2-: ft, b"rn ->< y.A-A

= /cin\, . nll + brnll. 1T/Z_

tl I ^t1.

fu__

FxA Jcl : Gox-; fa,ul4oln I i^s/tln a=2 , 4\

: f o,*tl7 ; n= 2,5..

- rl, l, :n14"

'**L -: a* J,-4 n-

: o .r -h.Tlq = Tlq.h

. f-orc-"r.iflf e nc0, po rn IV | "'t

f ["fu ) .-- ctn(rvu.n )11nXLt4r):

EJ(**t) ax

L= z_ C.n (J^. nlu) . a x

lr,= t i

{-r€L-

Y

x.o * '\Lbx

0+LLTT-- t4

?1 1:iln=- Cort Tlq Tlrt + Con + +': nlt ( con T1-n r Gntt2 )

0.7200(6tt74 .

6r :5 , 4x = thli -- rr lto

#* - p',+lt'4x- = kT/,0

J ( t6l^ ) : Con (Ja.n I r;) ,

An: =J,t=|j t"$.) 4 (

:- z_. Gn(_t+ rylo).ax*.=t L- ttv'

- n/,0 (hn'r1,e t An''t'], r ;so 3n/t0 * Loo 2TlS + Go n t z): 0.917 (0 t gTq .

/1")t. I - -''&s Jtnl-t fa,al :1,,2);T):2.ooln ! -n=2,

At- =+ = +:_ . r.7.& = ,Io i _0t .a K

7\2 = t+2( 5)..2^llttn =- -, l (-1").oo

-[n= i

Z: Z -L-.4rt'l'r = t ]('q

t..

=T'E( l) * i(r)t5-T, L

35__6

= 'e9333 .

4.

r,t7. JE)= \Ir,,(tbol6\ ? roLrn fi=Z

, fa,bJ'lr>,r4Y- = 'l?

0t ,0t17- lr l I

j [x"r^ ) -_ Vr _ r4%-

=!fii22 t

Izt_

)!g:rr

?

= 0.Lt 39012 L

ag4un T\=D ,()\- =r/fxNlr. : Jrlt

--,0 t5Az:

.lt= t

! 29 --o^t-?

I

at')

t-

- tl2O .-i , "'iz1.r ,--_-_ 5 q ' g -;.;

= 0'6592C22

l-t \25 -ls, t^t

rl zo -l 2s-15

-t

[xto.

5oln :

J el dx-

B l"fl = 3[rr)

=- 3 : j(4

1t^l =s) fa,n] = fr,ff'T\neJ Jora,u

^, ,),(.

I = j'aa"IL| = 5 lnlnl'-L| =5(x_z). _5;_roI

I A'(*) - a = jt"lI P-,

lY*t =J(r) = 2x+2 ; [a,N] : fiqI lxlo 1-;'i [u l-71--, jI

I

I 1},t ruaruruA ^rLLq-

ia E A- 4,aplZoid.

ry A in -W ^ru^, jktn

,

nG) =+ [(2x*z)*2] L .ri+2rFh,ta, c}'

. ,l,,-

lr .apr26 r{

2._

? ..^- ,lrv, uf,'t'o 'nFon fl"/fi n F-l - -€ [*)ftn

,:!

U

D*-j:KGtw*

= zJ+ *t)a{dx-

:= 2taltl+3r**L M̂y^

["/r'L'''*'ft {*fq'/"

( )t*-vz u; ) e

=i)+ - {z )uo u-- ili\tlt - rlz u4 *c

A,,,_

2t |IUu,".x--+ 2con9.,^

i:- Jouinx-d(+ )tanxd,t

JA= - 4Gnx- f 2 5inx_ +-C d_ ,a--

22 . ) tu t"rl* + Grw"t-Co-t ,t ) drt

-- 4lOn"tx_dr + lA*cx.Glx M<*) )""

': 41an x- An-tct_ + C &_,

2s - )c** (cou+ Jan,<.) dx-

: )

bacL x-d* + ) soc x-. tann cJrr

=- *lan it- + bttx* + C d"_,.

,'-'-'\

5rc*[+un l- + Cnnt) drc

J!,*olanx- + o,/n */-) dx-

: lsnt-)onx-d,,. + [ol ^-)---- )

= bte-X-+K+e Itl&*,;2s I u:"9

dA) Gn&

-- I seel.'5actr d&J

: )sdv da-

= lan0_+o A,.,,.,,

z6.l d{J Coaay

=- L': JsinX

dg

: _ (any toU 'u M-

z? . I s;ro_. )ffirdti= ) {anx- Sacx dx-

= btct+O' /&,n,.,

l-li*;ffi;a- I

z9

I:lqaq + 2l atPJ J sta7e

oLr- -T + 2 )r*c2cp acp

6'L--T+ 2(_atco) +c62-= "Ca1e +c_L z

drr,

sinL&Gn0 ) d&

t-+ ) siat (9 Gny clg.

) uLd,-a

&" -, (')

6,)

A#L+c-M.:

JL,*

J*&+

Lo-[ ,

SinF : u*

Gnrl d8- = dup-0+

d+

s ' /--qltz^ ,J -A;;- uL-

--JeWa*: *,

Jsinx-drq: - 2Canx-+C-

€v - (")

;--J/^ffi- i'""r't b 7 "^bfu'tutf"o6'n

Lat) P = Q-ExL

=) clP-/ tn _ -10rt

xd,t - - 4e-,0

- -r I dPro I vF-

- | ,-'/2't ,nl0 -tl)+l -'

*^, p_on), ,,ur_ =

19. I xL,:a)L'\ 13+ t

3vF-

^-t lz+ll-

-'12*,

I x3+ , )"'

lr-g,r)E dt

dPD1--I

-) +lP

+L \M.-

I l, .^ otl/Lt [', -5tt- ) +C_

A-^

Lo-l ,

"tt3+l = i?

=) 3xL drt -- dP

xldx- = d P/b

Lo-l

dp

2.6,)

2- ---=

J

-lr

-l6,)

i

2tr)

+(-

+C

'l-3x=P

-)dt--,

-2+tI

&"^-r^(-39 +C.

2')

I I dP-T-)- ps

^-3rl- I Y _tpn- *r 'Iu

re t+-i-* I \-.

2? . J. .^ [sxr) drt

=tbnPclP

:. f o;ne +c

= i ein[Jrt) +c

Lz[,4xL*/ = P

-) 8r ct1 - d-P

rdrc - d? /g

P = 5inx-

. dP : Conv,dx

@,ct+ r)3

&.-t

-

A*.,' .--

olPdzt 6x-

23 )L5nru conx- dr

: jue a+

- tP +C-

= ooint- + c_ &", >*

L!-l ,

2tr. )*# ar

= + j"Pd e

=it?*Q-L-f

=- i un +(-

Lo't, P = rcQ

_) dP-"' A,L =

? 'x3 ax

q*d8

Lr

AJr,n I

25. l^ru-^'i;)

Ltl , af : -2x'

-\ djc-T : - 6r(Ld2t

. x?ax --+-,6

A-t

Lo-|,ot:

=\ dP( -dt\_

dP

2s. I 3*(-,(J&dt

=)"'4: -+ o?*L

= ldrI)?

-= 0^nlPl+ c-

: ln lat_r-nl

27.t d(e' )i&d'q

dr.----t + ?-

- - I -?xb- Ze- +c

&rL= o*\+L-'(

- LoI* e- ^)a,t

Lll ,

Khfr, +

=- l^r,-'P+c-

=- .lan-, (at) + C

?=[dp = dLdN-

l-lana , t* __(o9-

P=)-I d* -- d?/z

I

2 tdP) 1* p,-

t*,n-' P*c

+ +atr,'(Jz)+c.

A"-

t-ol

A-'/-

5.

3o)

ryil: I u'€ r,) -5=?(:c'nP)oc: i t"n [o/rt) +c /il_

boqz {lc dt{T_

= z [ 4o-cLp dp)

: 2 JanP+C- :

lanP + L

*nn [rto) + e

,: ;,.

=; dP n -1-/ iZ = -5,L-dx - -dI-xL^ -5

i\:aL

3xL

x"drt

Lo-l ,P ': 2-lintt$

=\ dP-) tf = - con4axq

.-\ - dP:/ -

= 6n4ode-

2 4^{\ W +L

P=[x- -y 3! = I'dr 2{x_2dp _ dI' llL

gt. 5r-rl[xo) dlt

5rc2P dP

[*")

*)

I

3I

o)

Lo-l , ?= tp

=)€:Ctc

dP =aL)

Nr"n :

q{ J a^ 4& fi- jin,io- d t9-

= -+ lwaP)/

- I ,Tlt- A=

t _ _Lt_t-t bh --

= + p- binhof''**

*),'

-, t-T -Z

. -l t-E- u

I s;,9 s

coos tl- ^in

2)- d*

?3 aP

?Ll-)- + c-(-l

6oq ll +C-.

Coo 3] d}

Ll-l ,

CrnZL =P

=) 2bin2*

,in Zt d*

5i0Sf=p:) 3Can39 -- -dfd+*) Gn 3* 4L = -f3

Lo-l ,

0+ GnTV : P

5;nt0- dp _ =dfL

Lo+ .' {an Et =P

:) bo-tltx- d{ = dlc

=#dl-

_ -dfL

Lo-F

t lPta- -'16^Ogl'n

3 -T- -r \-

: + @ bin63\+c

34 . I l;o zg ^ro) @+ ao zo)e av

ldP)-rt-

P-i+r +

I

--- -TL_tr [a+ c,,n2a)L

' u

36 - |r+*r'tr 5oout d,^-)

)

: ?11+C-

A-n :

C_

q

I

Itt+(hnt? 6u

kt fzAtlE,,^-r--E-V r -- larilr,.*

=. t drr----_r ! '-Pt-

- -l ^

= bin-' ( +^n ,J * c

sg. I sins d&J Crnt$+ |

I -dP) Pt+ t

= +^ntP+C-

= {e.n-' (un w) + C

,n J sqcs 2x- hn2ru dx

Lrl,k*

4Wtucrt-f

b4p, fanrt - P

) oql,l-dt -- clf

S.",

Lq-l ,

GorJ = P

-) siny dS -- - df

Lu) ,

bttTx -- P:tl zl):t,2

Ir

PzdP

* e3 +c-L)

brcS 2x:L&-

25r.c2x-lart2x = ffibo-c Zx{an 2x- drt - df

L-

'/

)

K .J Pin [oinCI)] c,:n& d&

lin p drc

CooP + e-

- C,sn [.ainu ) + C-

Lq-l ,

5in0 = P

ConF d0 = df

&"2--

Grrl

2e; "'l'1r)= pt+l

T= 4 ,Soln I

(a ) L"Jl

- tr6.

@) P,5IIJ mC poi"rrl- :

J (rtfa) ** e L?rL)+^LoH=Zlt

-{^=r r txt) 4\\l-l:

= (Sfn+ ?) t

Ji-= I

4tl= gZ _[+] Z 1.l*=l J.=t-'

_ t A!* +7^q

= 30+2&

= tg.

Ery-- 6.tt

) Qr=2 , b=G .

4x* -. ::---b- a 6-z

I

=J."end poin.{ ;

a*"&- '= at (_ft-,)ax: 2+ (A_r). I

-n- Jt+t

.J(*1t) = 3(*+r)+r = 31,,+4.4

EA:.

, (pl+e) ait =: 3* J4 + q !Jk-- t Jn= t

2t 4 (4+)un---Z-- t4x\ :30+16

*,lr_ = A+ &,a x- = 2tJ<_

| ':\tr.+?.

Ia)*fric

J (xff1.) = sel.-r )+rlt

^tA = J*1,j ("1^)'4(g ( 6J/.-z). I=-Z-L

"['t= t

ttr, = 6.z "L -22-

-11,t= | k= |

8a Jel5olfl :

(^) t4tY

t/x ;Ll

=- Z_-ll= t

9*rq

ar\d poin l,

&-,

A.: I , b:9

l [xtU") 4 (

:. "

(.{^- rt2) .ar,-

= 2 (],-'/2) I

= 2$.-1,

- 6!,.-Z .

poinl Is"

1(n-K

1.

A

4)( 2, Jtu3u ) =;U

=t+(&--L)L= 2trL* |

r q (q+ i5'---z-

j(x*t) :2$,- |

L

=, lt"*u) 4v-

.Ur- |

qr: >- rZ.Gt 2k-l

c2-Z:LI

2t.t -t 2x2-rL.l-' Z/,3 -l

.L* 7rq,

(b)

= 2+2/3+215 +zl72D')dJ L.--iItr

(c) 1v1id porrr{- x} = a- (-1. -tt2). 4\ .

= , (.r,- ,12)' 2 --a!^- t

RrSr^I ax\& poinf , x^L = ^+

h-a >c : t + Z-l<

i (",tu.) = 'I +zlt .

q

-1,,7,j ("Y.)a^q

-

I -z_ __. tL,0r.= t t +2h'

=2--z-l+2rl' t+Ztl '

2-erq3rf+Z-T- l4+o: lEi r= zee / rgg

A:

)2-tt2xl' l+2^\

A:9t4,t=t

)

q

-z--{rr.= I

(rtn) a tl,r2

W\-l

L-Lt-1\ r+t---a-

L,LT4 + T:i

..,.....'I

' ',:.,

a2(c) R,# - point " t!^.- cx+laaw : nlrr:l-

A = f,J(x*r^ ) 4v-

_ Z 6o (Tlq!r.) Tlq)*=t

= Conlrlq.nl4 + 6o(ntq.2) ntq+ (ao (ntrr,3)ntq

: r r), + coo (Try q' 'a)Tlq '

rt n/q*o_#.nU- t.Irlq

= _ irl4

A-,_32. Jt") = 21\.-xL; (=-t,b=g.bolni 4*=+=t

(4) 4f poinl. a-\ = a. r (1.- r) ax

: -l r-("U.-,).t

= -rr-0t_t

q = 1"-z

E +a*t^)a..: glzth.-z)-(r^-z)rJ r

=*)' ,^-q) q

^

_o,r=r - - fr, (&"- \!^.+u)

:1L*-q)+ (zrz-q) +(zx 1-r) + (2^q-q )j-l(,- q+11)

+ (zz-ur2+Q) t t 31 -tt x3 +q ) + (uz-ttxQ +,)j: (-zno+2+,{) - (r-g+ t*e)

: 4+2 =6

- l+J."1 : l+-r(

}("U.) = z(r+t*)- t,*r.)-: 2ilr- | * 2l^- )r,L-

: l_ L_ jr.L .

h ,.

.,[,t= I \

= (,-, -t>)+ (, -2-2r)+(, -s42)+(,-q -q r)E- * i * 5 - rt - 19

= _36

(c) rud axd. poiru$ , u!1^ = ^ (,r^- ,/z ) ax

= 4._ t/2.j(.ik) = 2u"'a) - (&_, tz)

= 2!^-t- l+L+&. - tl,t

= 3L - )*L - s'/'a

#,i (x*.1^ ) ax- - f ,(g-h ' \.'-rtq) ')

: (3 -*- rl Lt)+ ( 3 x2 - 22 -ilq ) +(: n3 -J'-g tq)*(s/,11-qz_?t)

- 1*-3-- , !-lL4' q T-q

= _ u/\ :_,

38 -g: 5J)r-; o-=6, ).=?

Soln 3 4x -D-o -fl-,- n --)lot

R,'# poinl ; x"L =- a+ fi']r(

= ft/'''A : A"o 'xl

x-, * E, J l*5^) 4,-

= !h,) # (l- a*6))?tnre+a", _h=t \- '

nr Tn

= Jern T lq.r _ t-lr. t )k)qt "[,t=l L' -n -- fr n ):H*?+# ! -?-#,r^J- j\* 1#n, -3 +l: fr* 1 'u

- Zs/z('* t^)\

.= 2r- 2' lz: nlz

M-_

Itsll1,.) = 5-"", ^:;, u: s

colni 4v-: u;f =31,

?,W poini I x!q: a+-fu_.arq

A= .lr-vn ,r)ri'e ,a ff,j (.lonq) 4,t

= H* f=,1 s-(etnf l3tn

= ,lrm ! { zt _ zt!.L \{ -)ru -l,t-t L n .61a /

= .h,n \+f ,-4LkzTt1 --)oo ( n I=f ' g7,pn=r^

)

=,!;i $n-# a(n+rXzr+')J

= .0.rn t )? Zl_.2n1+n+2ntt ?^r1 --)u I 6 6L )

=j!*1"- +('*+**')\= 27* 9

= t8

fvt. ( ^r

::1.' {r.; o, * I ,s f a) d,

=.?+l= 9(l^,) *7 lawoS

-{r, l"r, t'2ri?i)d,

-. It xdz r r(, 1rFdrJ" Jo': lz-"1{, ^x 4-n(n)\= Fl, T o(r 1- \/

,l_t5<-

(og

)-I '^-

-/J

OZ

+t

=. { (rd* - sIo*d.J -t J-t

= 4 [t]*ru S [rZq i:11 G*4 s (3 *)

I n /.\t^& (")

#"(A",

A. [n'' s; odoJ-afz

--p.ostl:;

: 0 (Avr5)

Jq . f"r, Sp.or&dU

= &^ojlo5-= La^rtq -fu"I

!1. [', e_,,Sxdrt _yq

= I5orrrl Yl(_ J _Tq

= !:zdr l"oct*a ^dr

f z" 1t fSrcxl L

C2-1D L )"

yq. fc sl-\d.xJW-

= Sivr-r/rn S;w?T)

L+L\2E=-. 2 .i+(lns\-!f-' ' )Js-. [' h - s,Lerknd Jx

Jo \

s Ibt-\dt-))-^z

FL'^l ol"

S lob n

L- v/

5aa -70

':]

(tus)\/

#-,(t hdr*, o/r(z

- -t- lL^ t, f'"z L - -rJr/.[z

-L - br.

,t/a_-LA

[,^

ln

k1=J_

2_tn t[T

= Siv,- r/t, S;w(-T)

J- + t\2 IZ=-' + = {e-(A\)

lj_. [, h _ s,e_e.knd JxJo I

= !:zdr {"act*aN^/tf z'1t fSpcxl Le2-1o L )"

= l+-o I r r L -1L"z -z) - L&t - c;srJ

a L- = *(4*)J4. (e s,-\d,t

J ln'P f )t-Td,=ol

) )'^'

c(\s2 l(*- LL

p4.

t"l(tus)\/

t6. (2 d^r-r

-

Ja\t;T:Lr,<oI 0.os- t t,r,l *L '3..1a

[*t-'CoS-1

-r/& _

4 obl ,L:S(C-&

dt = saestans d&

Id' =@*s-rzJ-lq )s@t7r,%s-i?A

€cS'Ya

T/t,1

dr7-1724

1ns' t Prsv/r-l

3A - 3n 4- ,.., Src.O = T -:aosl, 11.-/a- : it!^) ) p: €o -,/x-"

= ( )"^*So-1rffi

=)d& -- D- -

A{.[-vn/ 7- )-o

fe,

IeIu,A-

aJ

Qo

Qc

Co

it'

loS r ,/rJ_i:

)os- L71) ao5- t_ (2r7*\l\-,{-")

us.,

/ )

os - t 0-S ^/Ll CoS- L CoS ,q

%|n'Pn: --,.-/ frr,.^\'#- : 7ta 6*ns)

= gx{ [ru"J r, r ,-rr F".l: + ep '2]

r'

= C '- 9'^ o t afi-'1" - L- ,l

o !^\ /-

(o= € *RP,2 e.X _L_ 0 _ n{-& \

L .._ 5z *^'8_&-D.r

= G lft, -./T] # fe'^',. trrrliL {r.l: