## Calculus (3rd Edition)

$f(x)=\frac{x-2}{|x-1|}$ is discontinuous at $x=1$ and the discontinuity is infinite. The function is niether left- nor right- continuous at $x=1$.
Since $\lim\limits_{x \to 1}\frac{x-2}{|x-1|}=\infty$, then the function $f(x)=\frac{x-2}{|x-1|}$ is discontinuous at $x=1$ and the discontinuity is infinite. The function is niether left- nor right- continuous at $x=1$.