Calculus Examples

$lim_{x \to 0^{-}} \frac{x}{| x |} = - 1$

Step 1

Make a table to show the behavior of the function $\frac{x}{| x |}$ as $x$ approaches $0$ from the left.

$\begin{array}{c} x & \frac{x}{| x |} \\ - 0.1 & - 1 \\ - 0.01 & - 1 \\ - 0.001 & - 1 \end{array}$

Step 2

As the $x$ values approach $0$ , the function values approach $- 1$ . Thus, the limit of $\frac{x}{| x |}$ as $x$ approaches $0$ from the left is $- 1$ .

$- 1 = - 1$