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

Options

A. Continuous but not differentiable
B. Neither continuous nor differentiable
C. Both continuous and differentiable
D. Discontinuous but may be differentiable

Answer

C

Explanation

`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`