$$\lim\limits\_{n \to \infty}\frac{n\cos(n^4)}{n^3+\ln (n)}$$

I'm having trouble on how to approach finding this limit, but I do know the limit is 0 since $\cos(n^4)$ is just between -1 and 1 and $\ln(n)$ grows very slowly so for $n$ sufficiently large it will just be $\frac{n}{n^3}$ or $\frac{1}{n^2}$ and that converges to 0.