Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

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



Work Step by Step

\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}
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