Calculus Examples

$\frac{lim_{x \to 0} e^{x} - 1}{2^{x} - 1}$

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 $x$ approaches $0$ .

$\frac{lim_{x \to 0} e^{x} - lim_{x \to 0} 1}{2^{x} - 1}$

Step 1.2

Move the limit into the exponent.

$\frac{e^{lim_{x \to 0} x} - lim_{x \to 0} 1}{2^{x} - 1}$

Step 1.3

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

$\frac{e^{lim_{x \to 0} x} - 1 \cdot 1}{2^{x} - 1}$

Step 2

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

$\frac{e^{0} - 1 \cdot 1}{2^{x} - 1}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

Anything raised to $0$ is $1$ .

$\frac{1 - 1 \cdot 1}{2^{x} - 1}$

Step 3.1.2

Multiply $- 1$ by $1$ .

$\frac{1 - 1}{2^{x} - 1}$

Step 3.1.3

Subtract $1$ from $1$ .

$\frac{0}{2^{x} - 1}$

Step 3.2

Divide $0$ by $2^{x} - 1$ .

$0$