a) -d 0i1. (a(1aIo

6flJ36flJ3

20. a cost

/

i.v=(1+x+)(1+x)(l-x+) dx

c) 4(1+ )

cO

ojcuacv1oro .jorjaoZ dv

1

1+(1+x)

1 l+x+x

d)

=xab2.xb2v2.xe2-a2 .2 2 b2 2 2 _o -j =1

1woOQ1

a sfflt)

5a

-

1

(IV mi

I

+

i+-+

(s6n3o

t=iPJ2 4

=

1+

=

[

__i2 1+ti

1

y=as1nto (a)-tant.

J

__

LDemocrnampj 3. ionZolog1Om uiwoa nani,tm

a)-! c)1

1+

3eo

+

b) 0 d)

b1

7 C)..eX

d)

t0CT)x3

12. f(1)2 og'(2) = 4

=0

()1m3(.t= 0 Ml6aa 332_819

6(b)y=f(MLt)f()

x-+1

g(secx) m

(Iv dS/dt

dx

2

(x7+1)2-(2.x-1).2.a2

a)_L a) b) I2

u

2

-dx =2 0

(1)- (b:gbO)2

( J

xb (__j /

(a) 1

((-) a+b+c

1

'I" /

a2 0

(b) 0 (d) 2x ~1 1~x(2+xY0'

14.

c)L It)

o(36613O . g'(a)= 2, g(a)=b fog=I (xn o Identity Function)ms a1 f'(b)=

d)

)O S &,U3o f(X) cvQ)(Tfl 1662 qj91Ø1 oQ33o m

a)_L

of1 (x)

c61D&cZ -

=Sinx 2

- i)o?

dt1 +dtj

2+2x-2X2 (x +1)

'

(b) 0

b) 8 f6nno1eeJoo6rn(1nverse)g

1 13 u,1mt g1(x)=

f1(x) =

c

8 -

tans

tam;

-

secx

dx

cos'x

[cos 'x cotx_b0sinx]

9. Sn, 6mJo6))w161nor 6)1(0) 63

b) (55)c05'r

=

rruI1

(osr3(

fgr).g'x)=1

2sint cos 2

63la63)3(RJ36)2J

[cos 'x cotx+b01ns c) (S1fl?)c05 '5 cos's tans+b0)1l] (I)

6)6))30))36)

j

1

0 (r-1) ds (Ir n (CP6)s n-oo n(S_S1) S1) Ltn=S-S..j]

-a sint -

--a cost

(It -

dt hint < -a cost.

_

da

y=acost

dt

jno)

-

Sn

-

2y(l-2x) 2x -

xx2)(12x) 1:y=x_x21 .

°

dx/dt dl

=-f(t)sint+f'(t)cost-f'(t)cost-

cosec2t

=

A-B

tan"2-tan 11+tan 3--tan 1

2+...+ tan- 'xtan 1 (x-1) +tan (x+1)-tan .IC - =tan 1 (x+1)-tan' 1 dv 1 .

t cost

cosec tsect :3a 2 2

=

la

21 (h f(x)_3exf1 x)=6xex2x2 .. f (0)=3, f1 (0)=0 fl x)_2.xfx)+..f(0)._fl(0)=&xeX =

(1-a)(3-i) (n-x)+ + (1 -x)(2-x)......(n-1-x)J +01 = th x=b( 11(n-1)+0+ 1' 2.3.(a)fog =fog(x)=xx f(g(x))=x

'.dtj

+ '-

=.f'(g(a))=-1-1---= --

1f0)+1Ib0)12 dt' -'

zf1(b)(

17(a) 3x2 =3x2 tanxd[ .fx)=tanx]

r=1

3.2

If(t f(t)1 cost

=

I:ta1rA.tan 1 B=tan_l(T]

__

1 (3)-0=i a5 22. (b)y=(i-x)(2-x)..._(n-x)

f11(t)sint =-1f(t)+f(t)]sint = f(t)cost+f'(t)sint-f'(t)srnt+ dt

.

=

=-3acos2tsint

442

-

=

-

cosec2 t

=2x

f(t)cost 1 l+r+r2

dx

dx2 t=/

dv - dv/dx -

dt

[tan-tan'r]

(IX

cost

=2y(1-2x)

=2x2_3x+1 16. (c)

X

=

dx

dy I: -=1-2x1

tair1 ir'-ir]

=

jfl)

f(p)f1(X)f1(pj)f() f(x)J = f(nx)] 15.(b)u=2 =2 = - 2 dx

'

r=b

20.(a)x=asin3t=-=:3asin2t

dy

+S=nar11 -0

tan

2 dt

B0W0Jof(x)

fg(x) 1+[g,a)J =1+[gv)]3 [.f'(x)= -j--,I

(r-1)

-

OQ(TaOi '1

f(x)j.f(x)=f(nx)J(x)

0

)

Wa

n[f(x)] . f (x)=f (nx).n [f(x)J f1 (x1)=f1 (nx)

~ov

-I 8(a) g=f gx)=f x)f(g(x))r X6(1) %WO(O1 PJ1 .

a[_sint+_-r-_i-__4_]

Siflt

.

.

2

I22

a [_sint+_L] sin 1-srnt 1 a cos-t r = a

j1

d

tan

\ n =tan.11 tan0/2)= =--tan- S 2 2

2J1QmJoU

(1-sins)-

1o""--) =' th 2 F

=

(83 ffu6)W36m10886m136S

n-I)S0 + nS1 (n-i)S0-nS_1 (n-1)S (n+l)Sn+i

X 6(T)

siar+co.sx-1

r=1

Fb2ti1

I

18v_(sinx)cos

6om

a

r

10(b) y +

1 2sin0t2cosO/2

14(c) [f(x) j= f(nx)

I

-1

ost 2 b x= a (cU.

-

=

a) (sins)

=

..

.

d)

(a) b+[g(x) 1 / 1+[g(x)j3 [g(x)'3

fl J(361336)S (8)26).)

6)I)36)%

Urn 2f(x)-31(2.r) f() ' l2 c) [f(t)+f (t)] d) 63G)3CTD6) a) 3a b) 2a 17.Y =fx'),z = gx), f'x)= tans, c) 5a d) 4a I, x643uB g)=seoIo .2L dz b(b)y=(1+xh'4)(Ih1'4)(b+x) a) 2 =(1-x) (1+x) ser

+

(a) 1

)2o

=

=

(c) Sin(-22 2+2x-x1 X (d) LD6)M)3(rDaMgj I-Cosx

(x2+1)2

a) fI(er) b) f°(e )e +f'(e c) f"(e).e'+f"( ) 9. (b) S0 = d±-jII (r-1) S 16. x=f(t) cost-f'(t)sint y= f(t) sint+ V(t) cost p o %O d) f"(&).e'+f'( ).e = ar'-a 25. fx)monii niof°(o)=a r m woo1 ianiei1 (

2 12+2x-i-x(a)S12 (h)

=

(

b)2

2

a)2x+3x-1 b)2x2-3x+1 c) Zz + ls+1 d) -2?

6(T)2 6y = f(1)

SIlI.j)

x)1_si

wm1oo

2sin2O/2

tan4 (

2+2x-2.x2

- . ç2. - i

7(d)

-

(u+o+y)x0i1_l

+

dt 23. fog

=

th-_2 -iir

..dv_1

[.f'x)zsiiix2]

b) i)(n-1)! c) n'-1 d) ( 1)° '(n-i)'

-

c6)6m1

19 a)! b) 2

aicr? a) 0

• 3

[fx)]=f(ris) c) d) 3 3 2 1oZ f'(i-) f(nr) = 1a)fx) h) 0 c) fx).f'(nx) d)1 24. f 61)Juoa rs(Polvriomial) 15.y=x-x 8% mJou x 6)0) 6)o11o?, f(e )6)ao dx mwoo€iiy 6) n?o 6)86)6) (h)

5.

+

o t=0Z

6.)?

f'(x)a so

22. v= (1-x)(2-x)-----(n-x)6ao

d)-1--

13. y= x &_ x+7, x =f(t) .Q)cm1(a1

(10gb)(I )2

I f(x)

c)1

'2

-tan111--tan1 I-Coso tanO J sinO -

TFX -- j

(IoglO)2

X

dv 2 3 13.(c)y=x'-8x+7= 3x -8

=1 ...

I a)O

_1

1

______

=

secO

=

1+tan9

zan3.

s2.2

f1 (l)

-

f' x) -2.? fx +If(o)+f'(o)=

1f(tanx)cro (a)- (b0110)2 (Iog)-

1mio3J1

+

1-wooi c)21. x)

PJRMM16)ab O ule6)Qxm57

cot t

(c)( 0

x=tan0

4=gl(st1

b)2

3a

1-u

Q2S

i-X2

=

o x=-_.!L_o

x

(h) tant

+

log(sinx)

19. (b)

g'(seex)sinx

11 Y tan -cos '-f--

cotx.cosx-

(Sinx)

=

f1(tanx).Sec2x g'(secx).secx taux

(IU/dx

1

(cv) 1 (b) -1 (c) x (d) qx 2 x = a (Cost + log tanj_ )

OQ1u)1

12. (a) y= f(tanx) 4_=f'(tanx). Sec x du u= g(secx) . =g1(secx). Secxtarix '

b)

1+.r

1

b)

1,, 2(1-i-x) '3 d) 4(1+x2)

__i_,

dx

z=g(x5)=> d- =g l(x5). 54= 5.r1

dx secx [ ... g (x)=secxl . dy

dz

=

dy/dr

=

3tans:) 5x2secx5

dz/dx

18(b) - f(

1+(1+x2

dx-

-

ftl 5

2

-

f1(S) (2

li m 2f(x)-3f(2.x)~f(4.x)

o --

8J0

((Ul8oU3o -da 3(R(0T05)30

g(r)

dy - f(x)g(x)

di

(U38nJ,2J16>3(m3 Leoon1Qnauraibo2m0J6m

( \

ft (x)+ bogf(x). gt (x)] (Is (It tant 11(c) y = tan (-_eos'f!4 +-3(d) y=Iog .r a=bog.10 Sin'--) . cosx hi 1 1 y- (Sins) 1.4- udr =-= [.og,a=--] 1 =tan[(2tanu)+-9-(2tan'u)] Li -b ii . y- 1 S o -1 . cosx+ dZ z2 (1og.1q)2 = tan (2tan'u) = (Sins) sins -

Urn 2f"(x)-3.22f"(2x)+4.4f"(4a-) x-oO bim f°(x)-6f"(2s)+81°(4x) x-0 =a-6a+8a=3a F f (0)=al