Chapter 2: Limits and Continuity - Practice Exercises - Page 101: 46

$$1$$

\begin{align*} \lim _{x \rightarrow \infty} \frac{x^{2 / 3}+x^{-1}}{x^{2 / 3}+\cos ^{2} x}&=\lim _{x \rightarrow \infty}\left(\frac{1+x^{-5 / 3}}{1+\frac{\cos ^{2} x}{x^{2 / 3}}}\right)\\ &=\frac{1+0}{1+0}\\ &=1 \end{align*}