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If `[.]` and `{.}` denote greatest and fractional part functions respectively and `f(x)={(x((e^([x]+|x|)-2)/([x]+{2x})),x!=0),(-1,x=0):}` thenA. `f(x)` is differentiable every whereB. `f(x)` is continuous at `x=0`C. `f(x)` is continuous every whereD. `f(x)` is not differentiable at `x=0` |
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Answer» Correct Answer - D `lim_(xrarr0^(+))f(x)=lim_(xrarr0^(+))x((e^(x)-2)/(2x))=-1/2!=-1` `:.f(x)` is not continuous at `x=0` `:.f(x)` is not differentiable at `x=0` |
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