Let `("lim")_(xvec1)(x^a-a x+a-1)/((x-1)^2)=f(a)dot` Then the value of `f(4)` is _________

Let lim_(xto1)(x^(a)-ax+a-1)/((x-1)^(2))=f(a) . The value of f(101) equals

Let f(x)=sin^(-1)((2x)/(1+x^(2))) the value of f'(2) is

Let f(x)=tan^(-1)((x^(3)-1)/(x^(2)+x)) , then the value of 17f'(2) is equal to

Let f:R in R be a continuous function such that f(1)=2. If lim_(x to 1) int-(2)^(f(x)) (2t)/(x-1)dt=4 , then the value of f'(1) is

If f(x)=1-1/x then write the value of f(f(1/x))dot

f(x)=(3x^(2)+ax+a+1)/(x^(2)+x-2) and lim_(x rarr-2)f(x) exists.Then the value of (a-4) is

f(x)={(ax+2, x 1):} , If lim_(x rarr1)f(x) exist then value of a is :

" Let "f(x)=(alpha x)/(x+1),x!=-1" and "f(f(x))=x" ,then the value of "(alpha^(2))/(2)" is "

Let f(x) be a polynomial of least degree such that lim_(x rarr0)(1+(x^(4)+f(x^(2)))/(x^(3)))^(1/x)=e^(3), then write the value of f(3)

"Let "f(x)=x + (1)/(2x + (1)/(2x + (1)/(2x + .....oo))). Then the value of f(50)cdot f'(50) is -