Calculating the limit $\lim \limits_{n \to \infty} \sqrt[n]{4n + \sin \sqrt{n} + \cos (\frac{1}{n^2}) + 17}$ I am trying to calculate this limit:
$$
\lim \limits_{n \to \infty} \sqrt[n]{4n + \sin \sqrt{n} + \cos (\tfrac{1}{n^2}) + 17}$$
I understand I should use squeeze theorem but I am having some trouble applying it to this particular formula.

$\lim \limits_{n \to +\infty} \sqrt[n]{4n + \sin \sqrt{n} + \cos (\tfrac{1}{n^2}) + 17}$
$4n+15 \le 4n + \sin \sqrt{n} + \cos (\tfrac{1}{n^2}) + 17 \le 4n+19$
$\sqrt[n]{4n+15} \le \sqrt[n]{4n + \sin \sqrt{n} + \cos (\tfrac{1}{n^2}) + 17} \le \sqrt[n]{4n+19}$
$\lim \limits_{n \to +\infty} \sqrt[n]{4n+15} \le \lim \limits_{n \to +\infty} \sqrt[n]{4n + \sin \sqrt{n} + \cos (\tfrac{1}{n^2}) + 17} \le \lim \limits_{n \to +\infty} \sqrt[n]{4n+19}$
