Find the limit of the following sequence or determine that the sequence diverges. \( \left\{\frac{n^{3}}{n^{4}+1}\right\} \) Select the correct choice below and fill in any answer boxes to complete the choice. A. The limit of the sequence is \( \square \). (Type an exact answer.) B. The sequence diverges.

To find the limit of the sequence \( \left\{\frac{n^{3}}{n^{4}+1}\right\} \), we can analyze the behavior as \( n \) approaches infinity. We can factor out \( n^4 \) from the denominator: \[ \frac{n^{3}}{n^{4}+1} = \frac{n^{3}}{n^{4}\left(1 + \frac{1}{n^{4}}\right)} = \frac{1}{n \left(1 + \frac{1}{n^{4}}\right)} \] As \( n \) approaches infinity, \( \frac{1}{n} \) approaches 0 and \( \frac{1}{n^{4}} \) also approaches 0. Thus, the limit becomes: \[ \frac{1}{\infty \cdot (1 + 0)} = \frac{1}{\infty} = 0 \] Therefore, the limit of the sequence is: A. The limit of the sequence is \( 0 \).