Calculus Examples

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

Step 1

Simplify the limit argument.

Tap for more steps...

Step 1.1

Combine terms.

Tap for more steps...

Step 1.1.1

Subtract $x$ from $x$ .

$lim_{h \to 0} \frac{h + 0}{h}$

Step 1.1.2

Add $h$ and $0$ .

$lim_{h \to 0} \frac{h}{h}$

Step 1.2

Cancel the common factor of $h$ .

Tap for more steps...

Step 1.2.1

Cancel the common factor.

$lim_{h \to 0} \frac{h}{h}$

Step 1.2.2

Rewrite the expression.

$lim_{h \to 0} 1$

Step 2

Evaluate the limit of $1$ which is constant as $h$ approaches $0$ .

$1$