Chapter 6 - Inverse Functions - Review - Exercises - Page 506: 63

$$0$$

Given $$\lim _{x \rightarrow \infty} e^{-3 x}$$ Then \begin{align*} \lim _{x \rightarrow \infty} e^{-3 x}&=\lim _{x \rightarrow \infty} \frac{1}{e^{3 x}}\\ &=\lim _{x \rightarrow \infty}\frac{1}{\infty}\\ &=0 \end{align*}