If f(x) = \ x e^(- (1/(| x |) + 1/x)),x ≠ 0 0,x = 0. then f(x) is

(C) continuous for all x but not differentiable at x = 0

(B) continuous as well as differentiable for all x

(D) neither differentiable nor continuous at x = 0

Limit, Continuity and Differentiability: JEE Main 2003 Mathematics question

JEE Main 2003 · Annual, Paper 1 · Q4171

JEE Main 2003Annual, Paper 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002

f(x) = \left\{ {\matrix{ {x{e^{ - \left( {{1 \over {\left| x \right|}} + {1 \over x}} \right)}}} & {,x \ne 0} \cr 0 & {,x = 0} \cr } } \right.

then

f(x)

JEE Main 2003 · Annual, Paper 1 · Q4171

JEE Main 2003Annual, Paper 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002

f(x) = \left\{ {\matrix{ {x{e^{ - \left( {{1 \over {\left| x \right|}} + {1 \over x}} \right)}}} & {,x \ne 0} \cr 0 & {,x = 0} \cr } } \right.

then

f(x)