Examine the differentiability of following function `x=0,` `f(x)={e^(-1/x^2)*sin(1/x) x!=0 and 0,x=0`

Examine for continuity and differentiability, each of the following functions: f(x) = {:{(x^2 sin (1/x), x ne 0),(0, x =0):} at x = 0

Test differentiability and continuity of the following functions. f(x) = {(x sin (1/x), x ne 0), (0, x = 0) :} at x = 0.

Check the continuity of the following functions: f(x){(1)/(1-e^((1)/(x))),x!=0 and 0,x=0

The set of all points of differentiability of the function f(x)={(x^2 sin (1/x), x!=0), (0,x=0):} is

The set of all points of differentiability of the function f(x)={(x^2 sin (1/x), x!=0), (0,x=0):} is