Answer
$\infty $
Work Step by Step
\begin{align*}
\lim _{x \rightarrow \infty} \frac{2 x^{5 / 3}-x^{1 / 3}+7}{x^{8 / 5}+3 x+\sqrt{x}} : \frac{x^{8 / 5}}{x^{8 / 5}}&=\lim _{x \rightarrow \infty} \frac{2 x^{1 / 15}-x^{-19 / 15}+\frac{7}{x^{8 / 5}}}{1+3 x^{-3 / 5}+x^{-6 / 10}}\\
&= \frac{\lim _{x \rightarrow \infty}2 x^{1 / 15}-\lim _{x \rightarrow \infty}x^{-19 / 15}+\lim _{x \rightarrow \infty}\frac{7}{x^{8 / 5}}}{1+3\lim _{x \rightarrow \infty} x^{-3 / 5}+\lim _{x \rightarrow \infty}x^{-6 / 10}}\\
&=\frac{\infty-0+0}{1+0+0}\\
&=\infty
\end{align*}
