Calculus Examples

$lim_{x \to 0} \frac{x}{| x |}$

Step 1

Change the two-sided limit into a right sided limit.

$lim_{x \to 0^{+}} \frac{x}{| x |}$

Step 2

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

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

Step 3

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

$1$