Calculus Examples

$lim_{x \to 2^{-}} \frac{x^{2} + x - 6}{| x - 2 |}$

Step 1

Make a table to show the behavior of the function $\frac{x^{2} + x - 6}{| x - 2 |}$ as $x$ approaches $2$ from the left.

$\begin{array}{c} x & \frac{x^{2} + x - 6}{| x - 2 |} \\ 1.9 & - 4.9 \\ 1.99 & - 4.99 \\ 1.999 & - 4.999 \\ 1.9999 & - 4.9999 \\ 1.99999 & - 4.99999 \end{array}$

Step 2

As the $x$ values approach $2$ , the function values approach $- 5$ . Thus, the limit of $\frac{x^{2} + x - 6}{| x - 2 |}$ as $x$ approaches $2$ from the left is $- 5$ .

$- 5$