Answer
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.
