Calculus Examples

$lim_{x \to {0.25}^{-}} \frac{4 x - 1}{| 4 x^{3} - x^{2} |}$

Step 1

Make a table to show the behavior of the function $\frac{4 x - 1}{| 4 x^{3} - x^{2} |}$ as $x$ approaches $0.25$ from the left.

$\begin{array}{c} x & \frac{4 x - 1}{| 4 x^{3} - x^{2} |} \\ 0.15 & - 44.\overline{4} \\ 0.24 & - 17.36\overline{1} \\ 0.249 & - 16.12877211 \\ 0.2499 & - 16.01280768 \\ 0.24999 & - 16.00128007 \\ 0.249999 & - 16.000128 \\ 0.2499999 & - 16.0000128 \end{array}$

Step 2

As the $x$ values approach $0.25$ , the function values approach $- 16$ . Thus, the limit of $\frac{4 x - 1}{| 4 x^{3} - x^{2} |}$ as $x$ approaches $0.25$ from the left is $- 16$ .

$- 16$