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Evaluate lim(xrarr0) f(x), where...

Evaluate `lim_(xrarr0) f(x)`, where

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at x=0
LHL `=underset(xrarr0^(-))"lim"f(x)`
`underset(hrarr0)"lim"f(0-h)`
`=underset(hrarr0)"lim"(|-h|)/(-h)`
`=underset(hrarr0)"lim"(h)/(-h)=underset(hrarr0)"lim"(-1)=-1`
RHL=`underset(xrarr0^(+))"lim"f(x)`
`=underset(Xrarr0)"lim"f(0+h)`
`=underset(hrarr0)"lim"(|h|)/(h)=underset(hrarr0)"lim"(h)/(h)`
`=underset(hrarr0)"lim"(1)=1`
`because LHLneRHL`
`therefore underset(Xrarr0)"lim"f(x)` does not exist.
Let `0+h=x`
`rArr 0+hrarr0`
`rArr hrarr0`
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