Calculus Examples

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

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 $0$ .

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

Step 1.2

Move the limit into the exponent.

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

Step 1.3

Evaluate the limit of $\frac{1}{2}$ which is constant as $x$ approaches $0$ .

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

Step 2

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

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

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Anything raised to $0$ is $1$ .

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

Step 3.2

Write $1$ as a fraction with a common denominator.

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

Step 3.3

Combine the numerators over the common denominator.

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

Step 3.4

Subtract $1$ from $2$ .

$\frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$