Calculus Examples

$lim_{x \to \frac{1}{2}} x + 10$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $\frac{1}{2}$ .

$lim_{x \to \frac{1}{2}} x + lim_{x \to \frac{1}{2}} 10$

Step 1.2

Evaluate the limit of $10$ which is constant as $x$ approaches $\frac{1}{2}$ .

$lim_{x \to \frac{1}{2}} x + 10$

Step 2

Evaluate the limit of $x$ by plugging in $\frac{1}{2}$ for $x$ .

$\frac{1}{2} + 10$

Step 3

Simplify the answer.

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Step 3.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{2} + 10 \cdot \frac{2}{2}$

Step 3.2

Combine $10$ and $\frac{2}{2}$ .

$\frac{1}{2} + \frac{10 \cdot 2}{2}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{1 + 10 \cdot 2}{2}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $10$ by $2$ .

$\frac{1 + 20}{2}$

Step 3.4.2

Add $1$ and $20$ .

$\frac{21}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{21}{2}$

Decimal Form:

$10.5$