Calculus Examples

$\frac{lim_{h \to 0} {(2 - h)}^{2} - 4}{h}$

Step 1

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

$\frac{lim_{h \to 0} {(2 - h)}^{2} - lim_{h \to 0} 4}{h}$

Step 2

Move the exponent $2$ from ${(2 - h)}^{2}$ outside the limit using the Limits Power Rule.

$\frac{{(lim_{h \to 0} 2 - h)}^{2} - lim_{h \to 0} 4}{h}$

Step 3

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

$\frac{{(lim_{h \to 0} 2 - lim_{h \to 0} h)}^{2} - lim_{h \to 0} 4}{h}$

Step 4

Evaluate the limit of $2$ which is constant as $h$ approaches $0$ .

$\frac{{(2 - lim_{h \to 0} h)}^{2} - lim_{h \to 0} 4}{h}$

Step 5

Evaluate the limit of $4$ which is constant as $h$ approaches $0$ .

$\frac{{(2 - lim_{h \to 0} h)}^{2} - 1 \cdot 4}{h}$

Step 6

Simplify terms.

Tap for more steps...

Step 6.1

Evaluate the limit of $h$ by plugging in $0$ for $h$ .

$\frac{{(2 + 0)}^{2} - 1 \cdot 4}{h}$

Step 6.2

Simplify the answer.

Tap for more steps...

Step 6.2.1

Simplify the numerator.

Tap for more steps...

Step 6.2.1.1

Add $2$ and $0$ .

$\frac{2^{2} - 1 \cdot 4}{h}$

Step 6.2.1.2

Raise $2$ to the power of $2$ .

$\frac{4 - 1 \cdot 4}{h}$

Step 6.2.1.3

Multiply $- 1$ by $4$ .

$\frac{4 - 4}{h}$

Step 6.2.1.4

Subtract $4$ from $4$ .

$\frac{0}{h}$

Step 6.2.2

Divide $0$ by $h$ .

$0$