The left hand limit of the function f(x)=|x−4|x−4,    x≠40,    x=4 at x = 4, is

we have,(LHL of f(x) at x = 4)  =limx→4− f(x)=limh→0 f(4−h)=limh→0 |4−h−4|4−h−4=limh→0 |−h|−h=limh→0−h hh=limh→0 −1=−1. To evaluate RHL of f(x) at x=a i.e, limx→a+ f(x)  we may use the following algorithm