Question

If f(x) = {(xe^{-(1/|x| - 1/x)}, x ≠ 0, then f(x)), (0 , x = 0),is

(a) continuous for all x, but not differentiable at x = 0
(b) neither differentiable not continuous at x = 0
(c) discontinuous everywhere
(d) continuous as well as differentiable for all x.

Answer 1

so L.H.D ≠ R.H.D at x = 0
Therefore,  f (x) is non differentiable at x = 0