Calculus Examples

$\frac{lim_{h \to 1} h^{3} - 1}{h - 1}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $h$ approaches $1$ .

$\frac{lim_{h \to 1} h^{3} - lim_{h \to 1} 1}{h - 1}$

Step 1.2

Move the exponent $3$ from $h^{3}$ outside the limit using the Limits Power Rule.

$\frac{{(lim_{h \to 1} h)}^{3} - lim_{h \to 1} 1}{h - 1}$

Step 1.3

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

$\frac{{(lim_{h \to 1} h)}^{3} - 1 \cdot 1}{h - 1}$

Step 2

Evaluate the limit of $h$ by plugging in $1$ for $h$ .

$\frac{1^{3} - 1 \cdot 1}{h - 1}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

One to any power is one.

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

Step 3.1.2

Multiply $- 1$ by $1$ .

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

Step 3.1.3

Subtract $1$ from $1$ .

$\frac{0}{h - 1}$

Step 3.2

Divide $0$ by $h - 1$ .

$0$