Question

Evaluate the following limits:

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

Answer 1

$$\begin{gathered} \underset{x\to -1}{\lim }\left(\frac{x^3-3x+1}{x-1}\right) \\ =\frac{{\left(-1\right)}^3-3\left(-1\right)+1}{-1-1} \\ =\frac{-1+3+1}{-2} \\ =\frac{-3}{2} \end{gathered}$$