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If f(x)=sin|x|-e^(|x|) then at x=0,f(x) ...

If `f(x)=sin|x|-e^(|x|)` then at `x=0,f(x)` is

A

Continuous but not differentiable

B

Neither continuous nor differentiable

C

Both continuous and differentiable

D

Discontinuous but may be differentiable

Text Solution

Verified by Experts

The correct Answer is:
C
`RHD=lim_(hrarr0)(sin|0+h|+e^(|0+h|)-(-1))/h`
`=lim_(hrarr0) (sinh)/h-((e^(h)-1)/h)=1-1=0`
Similarly LHD`=0`
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