Problem 85E

85. (a) Use a graph to guess the value of the limit

$$\lim _{n \rightarrow \infty} \frac{n^{5}}{n !}$$

(b) Use a graph of the sequence in part (a) to find the smallest values of $N$ that correspond to $\varepsilon=0.1$ and $\varepsilon=0.001$ in Definition $2 .$

Step-by-Step Solution