Exercise 8

Determine all of the values of $x$ where the function $f$ (given below) has discontinuities. At each value where $f$ has a discontinuity, determine if $f$ is continuous from either the right or left at $x$ and also state whether or not the discontinuity is removable.$$\fe{f}{x}=\begin{cases}\frac{2\pi}{x}&x\leq3\\\fe{\sin}{\frac{2\pi}{x}}&3\lt x\lt 4\\\frac{\fe{\sin}{x}}{\fe{\sin}{x}}&4\lt x\leq7\\3-\frac{2x-8}{x-4}&x\gt7\end{cases}$$