If f(x) = cases x e^ -(1/|x| + 1/x) & for x 0 0 & for x = 0 cases then f(x) is

JEE Advanced Mathematics question

If then is

Answer: (A)

For : ; for : . So

f(x) =

Each piece is continuous on its interval.

*Continuity at 0:* ,

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Question ID VK-110468