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)=(lncosx)/{(1+x^2)^(1/4)-1} if x > 0 and f(x)=(e^(sin4x)-1)/(ln(1+tan2x)) if x < 0 Is it possible to difine f(0) to make the function continuous at x=0 . If yes what is.the value of f(0) , if not then indicate the nature of discontinuity.

Let ("lim")_(x to1)(x^a-a x+a-1)/((x-1)^2)=f(a)dot Then the value of f(4) is _________

The function f(x)={:{((x^2-1)/(x^3+1),x ne -1),(P, x=-1):} is not defined for x=-1. The value of f(-1) so that the function extended by this value is continuous is……..

The function f(x)={{:((x^(2)-1)/(x^(3)+1)" "xne1),(P" "x=-1):} is not defined for x = -1. The value of f(-1) so that the function extended by this value is continuous is

If f(x)=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx,f(0)=0 then the value of f(1) is

Let f(x)=(log)_2(log)_3(log)_4(log)_5(s in x+a^2)dot Find the set of values of a for which the domain of f(x)i sRdot

Let x in (0,pi/2)dot Then find the domain of the function f(x)=1/sqrt((-(log)_(sinx)tanx))

Find the domain of the function : f(x)=sin^(-1)((log)_2x)

A function f(x) satisfies the following property: f(xdoty)=f(x)f(y)dot Show that the function f(x) is continuous for all values of x if it is continuous at x=1.