`Iff^(prime)(x)=1/(-x+sqrt(x^2+1))a n df(0)=(1+sqrt(2))/2t h e nf(1)` is equal to `-"log"(sqrt(2)+1)` (b) 1 `1+sqrt(2)` (d) none of these

If f'(x)=(1)/(-x+sqrt(x^(2)+1)) and f(0)=(1+sqrt(2))/(2) then f(1) is equal to -log(sqrt(2)+1)( b )11+sqrt(2)(d) none of these

If tan^(-1)(a+x)/a+tan^(-1)(a-x)/a=pi/6,t h e nx^2= 2sqrt(3)a (b) sqrt(3)a (c) 2sqrt(3)a^2 (d) none of these

Differentiate log((x+sqrt(x^(2)-1))/(x-sqrt(x^(2)-1)))

lim_(x rarr2)(((x^(3)-4x)/(x^(3)-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(sqrt(x)-sqrt(2)))^(-1)) is equal t(1)/(2)(b)2(c)1(d) none of these

The value of lim_(x rarr2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2) is (1)/(8sqrt(3))(b)(1)/(4sqrt(3)) (c) 0 (d) none of these

If y=tan^(-1)sqrt((x+1)/(x-1)), then (dy)/(dx) is (-1)/(2|x|sqrt(x^(2)-1)) (b) (-1)/(2x sqrt(x^(2)-1))(1)/(2x sqrt(x^(2)-1))( d) none of these

intdx/(sqrt(1+x^2)sqrt(log(x+sqrt(1+x^2))))

e^(x)=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t)) andtan (y)/(2)=sqrt((1-t)/(1+t)) then (dy)/(dx) at t=(1)/(2) is (a)-(1)/(2) (b) (1)/(2)(c)0(d) none of these