`x=(6-sqrt(32))/2t h e n f i n d t h e v a l u e o f(x^3+1/(x^3))-6(x^2+1/(x^2))+(x+1/x)`

I fx+1/x=2,t h e p r i n c i p a l v a l u e o f sin^(-1)x is

f(x)=int_1^x(tan^(-1)(t))/t dtAAx in R^+,t h e nfin dt h ev a l u eof f(e^2)-f(1/(e^2))

E v a l u a t e:int(x^4+x^2+1)/(x^2-x+1)dxdot

If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b ,t h e n a is e q u a l 1/3 (b) 2/3 (c) -1/3 (d0 -2/3

If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b ,t h e n a is e q u a l 1/3 (b) 2/3 (c) -1/3 (d0 -2/3

: If f(x)={x^2+2,xgeq2 1-x ,x 1, 3-x , xlt=0,t h e nt h ev a l u eoflim_(x->1)f(g(x))i s__

Let L=("lim")_(xvec0)(a-sqrt(a^2-x^2)-(x^2)/4)/(x^4),a > 0. IfLi sfin i t e ,t h e n a=2 (b) a=1 L=1/(64) (d) L=1/(32)

f_n(x)=e^(f_(n-1)(x)) for all n in Na n df_0(x)=x ,t h e n d/(dx){f_n(x)} is (a) (f_n(x)d)/(dx){f_(n-1)(x)} (b) f_n(x)f_(n-1)(x) (c) f_n(x)f_(n-1)(x).......f_2(x)dotf_1(x) (d)none of these

f_n(x)=e^(f_(n-1)(x)) for all n in Na n df_0(x)=x ,t h e n d/(dx){f_n(x)} is (a) (f_n(x)d)/(dx){f_(n-1)(x)} (b) f_n(x)f_(n-1)(x) (c) f_n(x)f_(n-1)(x).......f_2(x)dotf_1(x) (d)none of these

Iff(x)=x+int_0^1t(x+t)f(t)dt ,t h e nt h ev a l u eof(23)/2f(0) is equal to _________