`lim_(xto2)(x-2)/(|x-2|)`

Explanation

L.H.L.`=lim_(hto0)(2-h-2)/(|2-h-2)|`
`=lim_(hto0)(-h)/(|-h|)=lim_(hto0)(-h)/h=-1`
R.H.L.`=lim_(hto0)(2+h-2)/(2+h-2)=lim_(hto0)(h)/(|h|)=1`
As `L.H.LneR.H.L.` the limit does not exist.