Calculus Examples

$\frac{lim_{h \to 0} (\sqrt{9 - (x + h)}) - (\sqrt{9 - x})}{h}$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $h$ approaches $0$ .

$\frac{lim_{h \to 0} \sqrt{9 - (x + h)} - lim_{h \to 0} \sqrt{9 - x}}{h}$

Step 2

Move the limit under the radical sign.

$\frac{\sqrt{lim_{h \to 0} 9 - (x + h)} - lim_{h \to 0} \sqrt{9 - x}}{h}$

Step 3

Evaluate the limit of $\sqrt{9 - x}$ which is constant as $h$ approaches $0$ .

$\frac{\sqrt{lim_{h \to 0} 9 - (x + h)} - \sqrt{9 - x}}{h}$

Step 4

Evaluate the limits by plugging in $0$ for all occurrences of $h$ .

Tap for more steps...

Step 4.1

Evaluate the limit of $9 - (x + h)$ by plugging in $0$ for $h$ .

$\frac{\sqrt{9 - (x + 0)} - \sqrt{9 - x}}{h}$

Step 4.2

Add $x$ and $0$ .

$\frac{\sqrt{9 - x} - \sqrt{9 - x}}{h}$

Step 5

Simplify the answer.

Tap for more steps...

Step 5.1

Subtract $\sqrt{9 - x}$ from $\sqrt{9 - x}$ .

$\frac{0}{h}$

Step 5.2

Divide $0$ by $h$ .

$0$