. Express the following as definite integrals and evaluate the limits. \lim _{n \rightarrow \infty}\left(\frac{1}{n^{5}} \sum_{i=1}^{n} i^{3} \sqrt{n^{2}-i^{2}}\right) \lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{n^{3}}{16 n^{4}-i^{4}}