Discuss the continuity and differentiability of `f(x)=|log||x|dot`

Explanation

`|-x|=x`

LHD=`lim_(h->0)(f(-1-h)-f(-1))/(-h)`

`=lim_(h->0)(|log|-1-h|-log|-1||)/(-h)`

`=lim_(h->0)(log(1+h)/(-h))`

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

RHD=`lim_(h-<0)(|log|-1+h|)/h`

`=lim_(h->0)(-log(1-h)/h)`

`=lim_(h->0)(-h+(h^2/2)-(h^3/3)....)/h(-1)`

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