a) \[\lim_{n \to \infty} \frac{3n^2 + 5}{n^2 + 4n + 1}\]
b) \[\lim_{n \to \infty} \frac{n + \ln n}{n + 1}\]
c) \[\lim_{n \to \infty} \frac{\cos n}{n^2}\]
d) \[\lim_{n \to \infty} \frac{n^3}{n^2 + 1}\]
e) \[\lim_{n \to \infty} \left(1 - \frac{2}{n}\right)^n\]
f) \[\lim_{n \to \infty} n\sin\left(\frac{1}{n}\right)\]
