Problem
\( \lim _{n \rightarrow \infty} \frac{5 n^{2}-\sin (3 n)}{n^{2}+10} \)
Solution
Step 1 ：\( \lim _{n \rightarrow \infty} \frac{5 n^{2}-\sin (3 n)}{n^{2}+10} \cong \lim _{n \rightarrow \infty} \frac{5 n^{2}}{n^{2}} \)
Step 2 ：\( \lim _{n \rightarrow \infty} \frac{n^{2}(5-\frac{\sin (3 n)}{n^{2}})}{n^{2}(1+\frac{10}{n^{2}})} \cong \lim _{n \rightarrow \infty} \frac{(5-\frac{\sin (3 n)}{n^{2}})}{(1+\frac{10}{n^{2}})} \)
Step 3 ：\( \lim _{n \rightarrow \infty} \frac{5 - 0}{1 + 0} \)
