a) \[\lim_{n \to \infty} \frac{n}{n+1}\]
b) \[\lim_{n \to \infty} \frac{2n^2 + 3n}{n^2 + n}\]
c) \[\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n\]
d) \[\lim_{n \to \infty} \frac{\sin n}{n}\]
e) \[\lim_{n \to \infty} \frac{\sqrt{n^2 + 1}}{n+2}\]
f) \[\lim_{n \to \infty} \frac{n^2 + n + 1}{n^3 + 2n^2 + 3}\]
