Why is:
$$ \lim_{n\to\infty}n \arctan\left(\frac{x}{n}\right) = x $$
Wolfram Alpha provides a power series expansion formula which justifies this, but why can't we say the following:
As $n$ is getting bigger and bigger, $\frac{x}{n}$ approaches zero. So $\arctan(x) = 0$, therefore this whole sequence approaches zero as $n$ approaches infinity.
Obviously this is wrong but why it is wrong?