The function `f(x)=e^(|x|)` is (a) Continuous everywhere but not differentiable at `x = 0` (b) Continuous and differentiable everywhere (c) Not continuous at `x = 0` (d) None of the above

Explanation

`f(x)=e^{|x|} `

`f(x)={ e^{-x}, x<0 `and
`e^x, x geq 0}`

For the continuity at `x=0`

`f(0)=e^{0}=1`

`text { LHL }=lim _{x -> 0} f(x) `

`text{LHL}=lim _{h -> 0} f(0-h) `

`text{LHL}=lim _{h -> 0} e^{-(0-h)} `

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