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Limits Continuity and Differentiability question

2003 · Shift 0 · Q73

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PYQ Library
JEE Main
Mathematics
Limits Continuity and Differentiability
2003 · Shift 0 · Q73

Limits Continuity and Differentiability question

2003 · Shift 0 · Q73

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

If

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