1.

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

Answer» `|-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)`
`=1`
RHD=LHD.


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