Evaluate limit as x approaches infinity of $\lim_{x\to\infty}\frac{\sqrt{x^3 +7x}}{\sqrt{4x^3+5}}$ I am having trouble figuring out how to answer this question by determining the degree of the numerator and/or denominator:
$$\lim_{x\to\infty}\frac{\sqrt{x^3 +7x}}{\sqrt{4x^3+5}}$$
I have tried deriving the first coefficient of the numerator and denominator, but not sure how to proceed to find the limit as $x \to \infty$.

Hint. You may write
$$
\begin{align}
\frac{\sqrt{x^3 +7x}}{\sqrt{4x^3+5}}&=\frac{\sqrt{1 +7x^{-2}}}{\sqrt{4+5x^{-3}}}
\end{align}
$$ then it becomes easier to obtain your limit as $x \to +\infty$.
