Calculus Examples

$lim_{x \to 4^{-}} \frac{| 5 x - 20 |}{x^{2} - 5 x + 4}$

Step 1

Make a table to show the behavior of the function $\frac{| 5 x - 20 |}{x^{2} - 5 x + 4}$ as $x$ approaches $4$ from the left.

$\begin{array}{c} x & \frac{| 5 x - 20 |}{x^{2} - 5 x + 4} \\ 3.9 & - 1.72413793 \\ 3.99 & - 1.6722408 \\ 3.999 & - 1.6672224 \\ 3.9999 & - 1.66672222 \end{array}$

Step 2

As the $x$ values approach $4$ , the function values approach $- 1.667$ . Thus, the limit of $\frac{| 5 x - 20 |}{x^{2} - 5 x + 4}$ as $x$ approaches $4$ from the left is $- 1.667$ .

$- 1.667$