Calculus (3rd Edition)

We are given the function: $f(x)=\ln |x-4|$ Compute the left hand and right hand limits: $\displaystyle\lim_{x\rightarrow 0^{-}} \ln |x-4|=\infty$ $\displaystyle\lim_{x\rightarrow 0^{+}} \ln |x-4|=\infty$ Therefore we got: $\displaystyle\lim_{x\rightarrow 0^{-}} \ln |x-4|=\displaystyle\lim_{x\rightarrow 0^{+}} \ln |x-4|=\infty$ As the function is not defined in $x=4$ and both its one-sided limits are infinite, the function has an infinite discontinuity.