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 right.

$\begin{array}{c} x & \frac{x - 3}{| x^{3} - 3 x^{2} |} \\ 3.1 & 0.10405827 \\ 3.01 & 0.11037405 \\ 3.001 & 0.11103707 \\ 3.0001 & 0.1111037 \end{array}$

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 right is $0.111$ .

$0.111$