Calculus Examples

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

Step 1

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

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

Step 2

Evaluate the limit of $f (x)$ which is constant as $h$ approaches $0$ .

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

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

Add $x$ and $0$ .

$\frac{f (x) - f (x)}{h}$

Step 4

Simplify the answer.

Tap for more steps...

Step 4.1

Subtract $f (x)$ from $f (x)$ .

$\frac{0}{h}$

Step 4.2

Divide $0$ by $h$ .

$0$