Test differentiability and continuity of the following functions.
`x^2 |x| at x = 0`

Test differentiability and continuity of the following functions. |1-1/x| at x = 1

Test differentiability and continuity of the following functions. f(x) = |sinx| at x = pi

Test differentiability and continuity of the following functions. f(x) = cot x at x = pi/2

Test differentiability and continuity of the following functions. f(x) = tan x at x = pi/2

Test differentiability and continuity of the following functions. f(x) = x/(1+|x|) 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.

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