= ,(" I x-t/" . ( t+ x)-

k) l" q,( 7'+ t= A

G) l,n nea ' /n Q+ e.

BAsrc

3 e.ryn

'x+l _- 2

n u** ' ?- ln z

z ^

= h L x ' . ( t +7 'S

- )/t !.n I2

= , !nx + l^e '= l n X

La; d 6cJfcet

Lou o

Lqrt

n e = |

+ T 1q'+r ) La,,c

pq (q' t I

La* 2L+ e't La,;- 3

Lo'e 4= q - r t ( > t e x

8 + L2

(8

Ln on b.'ffi Sioll-

- ! ,

- .loL1t laa3

Lo,,t 1 & Z

x ? l.r,*1

+ - 4 ) =

x(t- 4) =- > |a' - 4x -> l =-o

= ^ J

x = 7 &nCe-

(c ) loq ,n (q +L) - loq ,^ k -s )

= l o: l o ( x 4 )

d + b = l o q , - 3 o- c ' l x = - 3 L

(a) a ln (q-D = ln h,"-5)h -t)' = l n ( x ' - F

( q - r ) ( r t - : x 2 ^ g' - z x * l = d t - g

->x r ' - L

x = 3

Lq*

La;1

-1)(q +3) = o

Lo,c.

e ' n = etr 2X)h e.) x > (ry'- 3)

>r ( = (q - - '

a t * ) q - 3 = a

k -3) (x + lX = 3 o , l

3 t t 3 -

x - - - z

3x,' = ) + I 1x

31 ' - - - z

= t oq = 3(p)' = 3 o o

(d) x-- %

q-- n)x = r )

5 .= 3 t = 2

(e) ln(2A-L) - = lnxn(x^r

( r )

= /

) x - > = X (> x - > = , _ xaz - )q +z z c ,( q - r ( q , 1 ) = oX - - ) o Y X = lX - > ( g i < - - q , z

r

-TTEW

"lft+

4 -+ X'Gx

* 2 %D

2x,

fla6 y ' / '

s -'/z -r-q,

g/> -qL

' - > o = o+ ? . ' - > o - - o

q ' - > D = o

(q')' + v' ^ )p =- o

t a t u = 1 '

U > + U - L o ' - c )( u + r ) f u - 4 ) = o

u = ' U t r q = 4

+

'i - ) -

= xn. . x

(a)

( D q 1 , , '

= I . ( g ' * - -'q'(x1"1-t

' 'u ' (qa, q--K

6JW z l l -= X ' . 1 . u ' t l

\ = )

(s thca x 'Z o

( b )

( c )

(e ) ln

Lil T;

$ )

( ) = - l

d = e ,

2 e e + l n ( t )/ = e e + o

o?- e',

n (a) e ' - q +lnx-_ 7 +h > o

x - - x + t > O

* X - - L l q + | = O( > x - t ) ( ) % - t ) = o

= / z

= (e - r

+3 t i - f * t 5

= )( 3)' + 3())-- 3z f l) + lS= gU + r7 -q ( +E = e

Su u- 3 ) = o . ' . (x -z) r i - the c.ltf o

l "n dr'yrSr ( olher m e'thods ean be Qoote

2x-+1x - 51 - 3 2)tt + ) x" -3zx +t.{

zq' - 6q,'q-- 32

2 _2 lx- 9q+E

b) -Sr +ty

h -g\(tq(' x -.9)= oh-t) ()x-t (x tt) =o

= o , ) x - l r o u 4*-h>a

(-)

k) Ja -32

- 3

= t/z > - g

0$€ e silbs'hLd in ov el *n ti qh'orl ne'f\' od

Jr ulve. fteve bshl-,titon vne*l od ls vr)

+J- = t 3 + 3 q = 3 3 - J - lt /

7 : 3 ( : a - c ) - ( D

- 3 = t S q G

SrrU h) rifu b)

- , =F5( 3 3 - 5 - 3 u

= lE -_ t - -rt

= 3

R^{- - 3 t h i z ( t ) o r ( z )

( t g - (33 - scry, g ) = 6

Gord,m a|-e- e tilet sech'"r'r ( 6

rrtr

(b ) For l,i x ) =) x + g = " q , ' + X - lq-+ x- 2q - I -F=o2( ' -A -6 = - o( q+D(z -3) :o

firt ( -> ) = )1 ->) +5 = I( 3 ) = > C a ) + 3 : l l

Inlws ee*o n ,v.lS l ) a^ol (3

L"t ? r y + b

h ) = - a L -

Fztr 61en x) :-' i 6 t t

>q-+ro t = e)z (q(+5A , = - o ( N d = ^ e

fo) ==t6co)

t -(-s) = (-E 't (Fv : ) J l - ? o t = 4

lnlegact'*1 rvr& &te (o,1)

u )

( c )

= TR( - T c (+ lo - ( , + 3 +tl+l 0 - , - 3 -+' + .F ,+ 6

t bruk-e" It --o

' +{, + d = o

L t -- - 5

= ( (sie- 7 r o

the braakcvor't I r-s

d n , = d s t->.o ++P, t P, = + 6

31 , tP t =1 f , n)

= &s,- /:. +_r 4p: = ] t -L

?, -z

9&n< ( t) a"d c2 St*t, H4neo

*LP , = 5z-)F' = I

- ( t )

; E\;nhq*a Pz '. 0) Y> t.:)

= L L =)'r = 6

To

.rl P,7 ( "L I

r fD ,:" (>)

P r = > 5 - 3 P = > b - > ( ( ) - 8

ind ' f rb nLt'? "hh'e"

& . , = P 1 6 ' - A t 6 = l zQ r = 3 t + . L 7 3(8) 4a = >L

= x"+ - B ? + + 4 0

2 - l

-4) >o

= * f , C J f D =

( s,i ro >.o)

= (tt-)'+L( + - p = t 6 t 8 - g = / (

c^d Quan{ M - 4 a n

x) = qG)x ' - B x = ' B x - l L - x L

)x- - t61 +l) = o> ( x " - 8 " ( + 6 ) = o

a , ' - 8x+6 2 o

+ C = Q

ili bnr., m

f 6

Put |.i-f-z

t/lcs-

a = l b = - B < _ > 6

(-e)'-4trt (0>(t)

6+-

4o

8 zJl6

= + +

*\e 6larsec4;"rl oin ts

k = Pr>tlo =' + 3 -7o = o

.f lo 4= - l o

z

Gr< to ar'reA

) o

t - to = 11 .

q.rG 17 ond -T

.

t{to

F

1b"I

a&m&c

- c ' P

tLe + td 3+ ̂ 24 - Q ,+ 2 2

lq" +bs'+ / :d + zQ, + z- 3 9 >

, +O -32 = q)

) = oYe'+ tB&, ( P = Q

L =5L c = - 7 L g

>L9(ts(n')&

)(r4 . t7 . 2

>(r(x)

2(s) a(F) B

: $ ( sti< & 7ro

(s) +2

t U

I o a n d B

6sg5

'+g(a,-7 ff=o+1/,) ( e- g) =o

6o= 8 (g'iq&>ro

& r - J

P = l;tu-i-

Nfo*e ,llrqfa^A uQnil

rh -ft'

trilr-12p1

P^t

1',e 'lrb"4

C-o+X * *anx =( i*m L.d.S

*an = 9ec cAsec

o. Id.en

Setx = 6**nx =

I

lo,nX 'T

Os = &0 - z

= l o -+Lp - ?o =rr_ c.lO =_e( o+ to ;^ =sc r f D? - l o

( s6cs ?zO

- l = I

Uand a E

ztec X

sa l*anx

, 9<c

t -

. Scc

1Y-l

F,r'1 LHS

fwn Le+s :

( sth x -r as x)'- ( s,i,y +casx) (gir to,t7\ aosX Z cosy

- l

29iXa> -t r-os"x -l

r1&- Sw't "=f I ut s'X = J

2 a x V r'Sriza - 12 r-qx

= ) 9 / i aos t - l\ c n s /

= X 9riqXry{x

6scr *Sr; 7f

sti'x( a t x + t ) gn'r tas'z( = I| - ac'q gth-z( = | -as'-(

(c"sx 1t(l- asx

Cas' as4I - cosv | - cosy

t &i?.eosx + oosl

( u f x + c ,seax)

gn kx g[1 hs + .91,i

= g f i X

= *an

cD SX eos

( Pr.re)

* gfas/ft4 t agx et>shs^ gti c4 + qsT 4s

t ; )