Question

$\underset{x\to \infty }{\lim }\frac{5x^3-6}{\sqrt{9+4x^6}}$

Answer 1

$$\begin{gathered} \underset{x\to \infty }{\lim }\left[\frac{5x^3-6}{\sqrt{9+4x^6}}\right] \\ \mathrm{Dividing}\mathrm{the}\mathrm{numerator}\mathrm{and}\mathrm{the}\mathrm{denominator}\mathrm{by}x: \\ \underset{x\to \infty }{\lim }\left[\frac{{\displaystyle \frac{5x^3-6}{x^3}}}{{\displaystyle \frac{\sqrt{9+4x^6}}{x^3}}}\right] \\ =\underset{x\to \infty }{\lim }\left[\frac{5-{\displaystyle \frac{6}{x^3}}}{\sqrt{{\displaystyle \frac{9}{x^6}+4}}}\right] \\ =\frac{5}{\sqrt{4}} \\ =\frac{5}{2} \end{gathered}$$