Question

$\underset{x\to 4}{\lim }\frac{x^3-64}{x^2-16}$

Answer 1

$$\begin{gathered} \underset{x\to 4}{\lim }\left[\frac{x^3-64}{x^2-16}\right] \\ =\underset{x\to 4}{\lim }\left[\frac{x^3-64}{x-4}\times \frac{x-4}{x^2-16}\right] \\ =\underset{x\to 4}{\lim }\left[\frac{x^3-4^3}{x-4}\times \frac{x-4}{x^2-4^2}\right] \\ =3{\left(4\right)}^{3-1}\times \frac{1}{2{\left(4\right)}^{2-1}} \\ =\frac{3\times 16}{2\times 4} \\ =6 \end{gathered}$$