Chapter 3 - Applications of Differentiation - Review - Exercises - Page 286: 9

$$\frac{-2}{3}$$

\begin{aligned} \lim _{x\rightarrow -\infty}\frac{\sqrt{4x^2+1}}{3x-1} &= \lim _{x\rightarrow -\infty}\frac{\sqrt{4\frac{x^2}{x^2}+\frac{1}{x^2}}}{\frac{3x}{x}-\frac{1}{x}}\\ &=\lim _{x\rightarrow -\infty}\frac{\sqrt{4 +\frac{1}{x^2}}}{3-\frac{1}{x}}\\ &=\lim _{x\rightarrow -\infty}\frac{\sqrt{4 +0}}{3-0}\\ &=\frac{-2}{3} \end{aligned}