Calculus Examples

$lim_{h \to 0} \frac{| x + h | - | x |}{h}$

Step 1

Set up the limit as a left-sided limit.

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

Step 2

Evaluate the limits by plugging in the value for the variable.

Tap for more steps...

Step 2.1

Evaluate the limit of $\frac{| x + h | - | x |}{h}$ by plugging in $0$ for $h$ .

$\frac{| x + 0 | - | x |}{0}$

Step 2.2

Since $\frac{| x + 0 | - | x |}{0}$ is undefined, the limit does not exist.

$Does not exist$

Step 3

Set up the limit as a right-sided limit.

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

Step 4

Evaluate the limits by plugging in the value for the variable.

Tap for more steps...

Step 4.1

Evaluate the limit of $\frac{| x + h | - | x |}{h}$ by plugging in $0$ for $h$ .

$\frac{| x + 0 | - | x |}{0}$

Step 4.2

Since $\frac{| x + 0 | - | x |}{0}$ is undefined, the limit does not exist.

$Does not exist$

Step 5

If either of the one-sided limits does not exist, the limit does not exist.

$Does not exist$