Test the continuity of the following function at the origin; `f(x)={x/(|x|),x!=0 and 1,x=0`

Explanation

`f(x)= {x/(|x|)` when `x!=0` and ` 1` when `x=0`

For the continuity at `x=0`

`f(0)=1`

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

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

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

`text{LHL} = lim _{h -> 0} –h/h=-1`

Now,

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