Tính các giới hạn sau
1. $\underset{n\to +\infty }{\lim }\frac{2n+1}{5n+9}$.
2. $\underset{n\to +\infty }{\lim }\frac{n-7}{n^2+9n+2}$.
3. $\underset{n\to +\infty }{\lim }\frac{n^3-3n+1}{(2n+3)\left(n^2+7\right)}$.
4. $\underset{n\to +\infty }{\lim }\frac{n^2-9n+2}{5n+9}$
5. $\underset{n\to +\infty }{\lim }\frac{3^n-2^n}{3^{n+2}+1}$.
6. $\underset{n\to +\infty }{\lim }\frac{2^{2n+1}-7^n}{2^{3n-1}+7^{n+1}}$.
7. $\underset{n\to +\infty }{\lim }\left(-2n^3+9n^2+1\right)$.
8. $\underset{n\to +\infty }{\lim }\left(\sqrt{4n^2+2}-5n\right)$.
9. $\underset{n\to +\infty }{\lim }\left(\sqrt{n^2+1}-\sqrt{n^2+8n+2}\right)$.