Chapter 3 - Applications of Differentiation - 3.4 Limits at Infinity; Horizontal Asymptotes - 3.4 Exercises - Page 242: 29

$$ \infty$$

Given $$\lim _{x \rightarrow \infty}\left(x-\sqrt{x}\right)$$ Then \begin{aligned} \lim _{x \rightarrow \infty}\left(x-\sqrt{x}\right)&=\lim _{x \rightarrow \infty}\sqrt{x}\left(\sqrt{x}-1\right) \\ &=\lim _{x \rightarrow \infty}\sqrt{x}\lim _{x \rightarrow \infty}\left(\sqrt{x}-1\right)\\ &= \infty \end{aligned}