Question

$\underset{x\to -1}{\lim }\frac{x^3+1}{x+1}$

Answer 1

$$\begin{gathered} \underset{x\to -1}{\lim }\left[\frac{x^3+1}{x+1}\right] \\ \mathrm{It}\mathrm{is}\mathrm{of}\mathrm{the}\mathrm{form}\frac{0}{0}. \\ \underset{x\to -1}{\lim }\left[\frac{x^3+1^3}{x+1}\right] \\ =\underset{x\to -1}{\lim }\left[\frac{\left(x+1\right)\left(x^2-x+1\right)}{\left(x+1\right)}\right] \\ ={\left(-1\right)}^2-\left(-1\right)+1 \\ =1+1+1 \\ =3 \end{gathered}$$