## Calculus (3rd Edition)

The function $f(x)$ is discontinuous at $x=0$. The discontinuity here is neither jump, removable nor infinite.
The function $\cos \frac{1}{x}$ oscillates around $x=0$ and is discontinuous at $x=0$. The discontinuity here is neither jump, removable, nor infinite. The function is neither left nor right continuous.