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If f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne ...

If `f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne 0),(0 , x =0 ):}` then f(x) is

A

Continuous as well as differentiable for all x

B

Continuous for all x but not differentiable at x = 0

C

Neither differentiable nor continuous at x = 0

D

Discontinuous everywhere

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The correct Answer is:
B
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