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

Question

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

then $f(x)$ is

discontinuous everywhere

continuous as well as differentiable for all x

continuous for all x but not differentiable at x = 0

neither differentiable nor continuous at x = 0

Solution

Please login to view the detailed solution steps...

Go to DASH