Chapter 2 - Limits - 2.7 Limits at Infinity - Exercises - Page 83: 24

$\infty $

We have \begin{align*} \lim _{x \rightarrow \infty}\frac{\sqrt{x^3+20x}}{10x-2} &=\lim _{x \rightarrow \infty}\frac{x\sqrt{x+\frac{20}{x^2}}}{x(10-\frac{2}{x})}\\ &=\frac{\sqrt{\infty+0}}{10-0} \\ &=\infty \end{align*}