Let $f\left(x\right)=\left[x\right]+[-x]$ where $\left[x\right]$ denotes the greatest integer not greater than $x$. Then for any integer $m$

$f$ is continuous at $x=m$

$\underset{x\to m}{lim}f\left(x\right)$ exists and is equal to $f\left(m\right)$

$\underset{x\to m}{lim}f\left(x\right)$ exists but is not equal to $f\left(m\right)$

$f$ is differentiable at $x=m$