Compute the limit of $\arctan \left(\frac{1}{x}\right)$ as $x\to 0$

The limit of $\frac{1}{x}$ does not exist when $x\to 0$

From the left, the limit is $-\frac{\pi }{2}$; from the right, it is $\frac{\pi }{2}$. They differ: the limit of $\arctan \left(\frac{1}{x}\right)$ does not exist when $x\to 0$

▶Limit:   $\mathrm{undefined}$