# Chapter 2 - Limits - 2.7 Limits at Infinity - Exercises - Page 82: 20

The lines $y=\frac{2}{3}$ and $y=-\frac{2}{3}$ are the horizontal asymptotes of the given function.

#### Work Step by Step

To find the horizontal asymptotes, we calculate the following limit \begin{align*} \lim _{x \rightarrow \pm \infty}\frac{\sqrt{36x^4+7}}{9x^2+4} &=\lim _{x \rightarrow \pm \infty}\frac{\pm x^2\sqrt{36+\frac{7}{x^4}}}{x^2(9+\frac{4}{x^2})} \\ &=\frac{\pm \sqrt{36+0}}{ 9+0}=\pm\frac{2}{3} . \end{align*} Hence, the lines $y=\frac{2}{3}$ and $y=-\frac{2}{3}$ are the horizontal asymptotes of the given function.

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