How to find the limit of this function We have the function $$\dfrac{\sqrt{n^4 + 100}}{4n}$$
I think the best method is by dividing by $n$, but I have no idea what that yields, mainly because of the square root.

Dividing by $n$ is a great idea: Note that $$\sqrt{n^4 + 100}\cdot\frac 1n = \sqrt{(n^4 + 100)\cdot\frac 1{n^2}} = \sqrt{n^2 + \frac {100}{n^2}}$$
So your limit is, after dividing numerator and denominator by $n$:
$$\lim_{n\to \infty} \frac{\sqrt{n^2 + \frac {100}{n^2}}}{4} \to \infty$$
