Question

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

Answer 1

$$\begin{gathered} \underset{x\to 2}{\lim }\left[\frac{x^4-16}{x-2}\right] \\ \mathrm{It}\mathrm{is}\mathrm{of}\mathrm{the}\mathrm{form}\frac{0}{0}. \\ \underset{x\to 2}{\lim }\left[\frac{{\left(x^2\right)}^2-{\left(4\right)}^2}{x-2}\right] \\ =\underset{x\to 2}{\lim }\left[\frac{\left(x^2-4\right)\left(x^2+4\right)}{x-2}\right] \\ =\underset{x\to 2}{\lim }\left[\frac{\left(x-2\right)\left(x+2\right)\left(x^2+4\right)}{x-2}\right] \\ =\left(2+2\right)\left(2^2+4\right) \\ =32 \end{gathered}$$