Calculus Examples

$lim_{x \to 7} \frac{| x - 7 |}{x - 7}$

Step 1

Change the two-sided limit into a right sided limit.

$lim_{x \to 7^{+}} \frac{| x - 7 |}{x - 7}$

Step 2

Make a table to show the behavior of the function $\frac{| x - 7 |}{x - 7}$ as $x$ approaches $7$ from the right.

$\begin{array}{c} x & \frac{| x - 7 |}{x - 7} \\ 7.1 & 1 \\ 7.01 & 1 \\ 7.001 & 1 \end{array}$

Step 3

As the $x$ values approach $7$ , the function values approach $1$ . Thus, the limit of $\frac{| x - 7 |}{x - 7}$ as $x$ approaches $7$ from the right is $1$ .

$1$