Calculus Examples

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

Step 1

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

$\begin{array}{c} x & \frac{x - 2}{| x - 2 |} \\ 2.1 & 1 \\ 2.01 & 1 \\ 2.001 & 1 \end{array}$

Step 2

As the $x$ values approach $2$ , the function values approach $1$ . Thus, the limit of $\frac{x - 2}{| x - 2 |}$ as $x$ approaches $2$ from the right is $1$ .

$1$