Calculus Examples

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

Step 1

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

$\begin{array}{c} x & \frac{x - 3}{| x^{3} - 3 x^{2} |} \\ 2.9 & - 0.11890606 \\ 2.99 & - 0.11185557 \\ 2.999 & - 0.11118522 \\ 2.9999 & - 0.11111851 \end{array}$

Step 2

As the $x$ values approach $3$ , the function values approach $- 0.111$ . Thus, the limit of $\frac{x - 3}{| x^{3} - 3 x^{2} |}$ as $x$ approaches $3$ from the left is $- 0.111$ .

$- 0.111$