JEE Math Practice Question
If $$f(x) = \left\{ {\begin{matrix} {x{e^{ - \left( {{1 \over {\left| x \right|}} + {1 \over x}} \right)}}} & {,x \ne 0} \\ 0 & {,x = 0} \\ \end{matrix} } \right.$$ then $$f(x)$$ is
- A.discontinuous everywhere
- B.continuous as well as differentiable for all x
- C.continuous for all x but not differentiable at x = 0
- D.neither differentiable nor continuous at x = 0
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