" Test differentiability and continuity of the following functions "

Test the differentiability and continuity of the following function at x=0: f(x)={[frac[1-e^(-x)][x],xne0], [1,x=0]:}

Test the differentiability of the following functions f(x)=x/(1+absx)at x=0 .

Discuss the continuity and differentiability of the following functions given below

Test differentiability of the following function at the indicated points. f(x)=x+|cosx|at x= pi/2

Test differentiability of the following function at the indicated points. f(x)=[x^2+1]at x=-1/2

Test the continuity of the following functions at indicated points : f(x) = {{:((x - a) "cos" 1/(x-a)"," ,x != a),(0",", x = a):} at x = a

Test the continuity of the following function at the origin: f(x)={(|x|)/x ;x!=0 ,1;x=0