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) . Then the value of f(4) is_________.

Let f (x+(1)/(x))= x^(2) +(1)/(x^(2)) , x ne 0, then the value of f (x) is-

Let f(x)=(bx+a)/(x+1), lim_(x to 0)f(x)=2 then the value of a is .

Let f(x)=x+1/(2x+1/(2x+1/(2x))) Compute the value of f(5) .

If f(x)= 4^x/(4^x-2) then find the value f(x)+f(1-x).

Let f: R rarr R be a continuous odd function, which vanishes exactly at one point and f(1)=1/2 . Suppose that F(x)=int_(-1)^xf(t)dt for all x in [-1,2] and G(x)=int_(-1)^x t|f(f(t))|dt for all x in [-1,2] . If lim_(x rarr 1)(F(x))/(G(x))=1/(14) , Then the value of f(1/2) is

Let f(x)={(log(1+x)^(1+x)-x)/(x^2)}dot Then find the value of f(0) so that the function f is continuous at x=0.

Let f(x)=(ax)/(x-1),x ne-1 .If 10f(x)=x, find the value of a.

Let f(x)=lim_( n to oo)(cosx)/(1+(tan^(-1)x)^(n)) . Then the value of int_(o)^(oo)f(x)dx is equal to

If lim_(xto0) [1+x+(f(x))/(x)]^(1//x)=e^(3) , then the value of ln(lim_(xto0) [1+(f(x))/(x)]^(1//x)) is _________.