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.

I assume you mean the limit as $n\to \infty$.  In that case, the limit is easily seen to be infinity as follows:
The numerator scales as $\sim n^2$ for large $n$, but the denominator scales as $n$ only.
The ratio thus scales as $\sim n$.
So the limit as $n\to \infty$ will be $\infty$.
