Calculus Examples

$lim_{x \to 2^{-}} \frac{| x - 2 |}{x^{2} - 4}$

Step 1

Make a table to show the behavior of the function $\frac{| x - 2 |}{x^{2} - 4}$ as $x$ approaches $2$ from the left.

$\begin{array}{c} x & \frac{| x - 2 |}{x^{2} - 4} \\ 1.9 & - 0.\overline{256410} \\ 1.99 & - 0.25062656 \\ 1.999 & - 0.25006251 \\ 1.9999 & - 0.25000625 \end{array}$

Step 2

As the $x$ values approach $2$ , the function values approach $- 0.25$ . Thus, the limit of $\frac{| x - 2 |}{x^{2} - 4}$ as $x$ approaches $2$ from the left is $- 0.25$ .

$- 0.25$