Discuss the continuity of the `f(x)` at the indicated point: `f(x)=|x|+|x-1|` at `x=0,\ 1` .

Explanation

Given,

`f(x)=∣x∣+∣x−1∣`

LHL at `x=0`,

`lim_(x->0^−)f(x)=lim_(h->0)f(0−h)=lim_(h->0)f(−h)`

`implieslim_(h->0)[∣−h∣+∣−h−1∣]=1`
RHL at `x=0`,

`lim_(x->0^+)f(x)=lim_(h->0)f(0+h)=lim_(h->0)f(h)`

`implieslim_(h->0)[∣h∣+∣h−1∣]=1`

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