If `f(x)={(|x+2|)/(tan^(-1)(x+2)),\ \ \ x!=-2 2,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=-2` , then `f(x)` is continuous at `x=-2` (b) not continuous at `x=-2` (c) differentiable at `x=-2` (d) continuous but not derivative at `x=-2`

Explanation

Given that,

`f(x)={{: ((|x+2|)/(tan^(-1)(x+2)),if xne-2),(2,if x=-2):}`

(L.H.L at x=-2)=` lim_(x->-2^-)f(x)`

`= lim_(h->0)f(-2-h)`

`=lim_(h->0) (|-2-h+2|)/(tan^(-1)(-2-h+2)`

`=-1`

(R.H.L at x=-2)=` lim_(x->-2^+)f(x)`

`= lim_(h->0)f(-2+h)`

...