# Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 388: 123

$e^4$

#### Work Step by Step

Let $x=\frac{n}{4}$, then we have $$\lim _{n \rightarrow \infty}\left(1+\frac{4}{n}\right)^{n}=\lim _{x \rightarrow \infty}\left(1+\frac{1}{x}\right)^{4x}\\ =\left(\lim _{x \rightarrow \infty}\left(1+\frac{1}{x}\right)^{x}\right)^4=e^4,$$ where we used the formula $\lim _{n \rightarrow \infty}\left(1+\frac{1}{n}\right)^{n}=e$.

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