Infinity Limit problem This limit I tried to solve it but I can't I use l'Hospital but it didn't work. Could anyone help me to solve it? 
The limit is :
$$ \lim \limits_{n\to \infty }\frac{n^{2}+3^{n}}{n^{n}+ 2^{n}} =? $$

Hint:
$$
0 \leq \lim \limits_{n\to \infty }\frac{n^{2}+3^{n}}{n^{n}+ 2^{n}} \leq 
\lim \limits_{n\to \infty }\frac{n^{2}+3^{n}}{n^{n}} = 
\lim \limits_{n\to \infty }\left(n^{2-n} + \left( \frac 3n \right)^n\right)
$$
