Calculus Examples

$lim_{x \to - 4} \frac{| x + 4 |}{2 x + 8}$

Step 1

Consider the left sided limit.

$lim_{x \to {(- 4)}^{-}} \frac{| x + 4 |}{2 x + 8}$

Step 2

Make a table to show the behavior of the function $\frac{| x + 4 |}{2 x + 8}$ as $x$ approaches $- 4$ from the left.

$\begin{array}{c} x & \frac{| x + 4 |}{2 x + 8} \\ - 4.1 & - 0.5 \\ - 4.01 & - 0.5 \\ - 4.001 & - 0.5 \end{array}$

Step 3

As the $x$ values approach $- 4$ , the function values approach $- 0.5$ . Thus, the limit of $\frac{| x + 4 |}{2 x + 8}$ as $x$ approaches $- 4$ from the left is $- 0.5$ .

$- 0.5$

Step 4

Consider the right sided limit.

$lim_{x \to {(- 4)}^{+}} \frac{| x + 4 |}{2 x + 8}$

Step 5

Make a table to show the behavior of the function $\frac{| x + 4 |}{2 x + 8}$ as $x$ approaches $- 4$ from the right.

$\begin{array}{c} x & \frac{| x + 4 |}{2 x + 8} \\ - 3.9 & 0.5 \\ - 3.99 & 0.5 \\ - 3.999 & 0.5 \end{array}$

Step 6

As the $x$ values approach $- 4$ , the function values approach $0.5$ . Thus, the limit of $\frac{| x + 4 |}{2 x + 8}$ as $x$ approaches $- 4$ from the right is $0.5$ .

$0.5$

Step 7

Since the left sided and right sided limits are not equal, the limit does not exist.

$Does not exist$