## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 327: 14

#### Answer

$$\lim _{x \rightarrow \infty} e^{x-x^2}=0.$$

#### Work Step by Step

Since $x^2-x$ is always positive for all $x>0$, then we have $$\lim _{x \rightarrow \infty} e^{x-x^2}=\lim _{x \rightarrow \infty} e^{-(x^2-x)}=0.$$

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