Calculus Examples

$lim_{x \to 2^{-}} \frac{| 2 x - x^{2} |}{x - 2}$

Step 1

Make a table to show the behavior of the function $\frac{| 2 x - x^{2} |}{x - 2}$ as $x$ approaches $2$ from the left.

$\begin{array}{c} x & \frac{| 2 x - x^{2} |}{x - 2} \\ 1.9 & - 1.9 \\ 1.99 & - 1.99 \\ 1.999 & - 1.999 \\ 1.9999 & - 1.9999 \\ 1.99999 & - 1.99999 \end{array}$

Step 2

As the $x$ values approach $2$ , the function values approach $- 2$ . Thus, the limit of $\frac{| 2 x - x^{2} |}{x - 2}$ as $x$ approaches $2$ from the left is $- 2$ .

$- 2$