Calculus Examples

$lim_{x \to 3^{-}} \frac{x^{2} | x - 3 |}{x - 3}$

Step 1

Make a table to show the behavior of the function $\frac{x^{2} | x - 3 |}{x - 3}$ as $x$ approaches $3$ from the left.

$\begin{array}{c} x & \frac{x^{2} | x - 3 |}{x - 3} \\ 2.9 & - 8.41 \\ 2.99 & - 8.9401 \\ 2.999 & - 8.994001 \\ 2.9999 & - 8.99940001 \\ 2.99999 & - 8.99994 \\ 2.999999 & - 8.999994 \end{array}$

Step 2

As the $x$ values approach $3$ , the function values approach $- 9$ . Thus, the limit of $\frac{x^{2} | x - 3 |}{x - 3}$ as $x$ approaches $3$ from the left is $- 9$ .

$- 9$