Problem
\( \lim _{n \rightarrow \infty} \frac{n^{2}\left(\sin n+\cos ^{3} n\right)}{\left(n^{2}+1\right)(n-3)} \)
Solution
Step 1 ：\( \lim _{n \rightarrow \infty} \frac{n^{2}\left(\sin n+\cos ^{3} n\right)}{\left(n^{2}+1\right)(n-3)} = \frac{\infty}{\infty} \)
Step 2 ：\( \lim _{n \rightarrow \infty} \frac{n^{2} \sin n}{(n^{2}+1)(n-3)} + \lim _{n \rightarrow \infty} \frac{n^{2} \cos^{3} n}{(n^{2}+1)(n-3)}\)
Step 3 ：\(\lim _{n \rightarrow \infty} \frac{n^{2}\left(\sin n+\cos ^{3} n\right)}{\left(n^{2}+1\right)(n-3)} = 0 + 0\)
