Calculus Examples

$lim_{x \to 3^{-}} \frac{| x - 3 |}{3 - x}$

Step 1

Make a table to show the behavior of the function $\frac{| x - 3 |}{3 - x}$ as $x$ approaches $3$ from the left.

$\begin{array}{c} x & \frac{| x - 3 |}{3 - x} \\ 2.9 & 1 \\ 2.99 & 1 \\ 2.999 & 1 \end{array}$

Step 2

As the $x$ values approach $3$ , the function values approach $1$ . Thus, the limit of $\frac{| x - 3 |}{3 - x}$ as $x$ approaches $3$ from the left is $1$ .

$1$