Calculus Examples

$lim_{x \to \frac{5}{2}} - x + 2$

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 $\frac{5}{2}$ .

$- lim_{x \to \frac{5}{2}} x + lim_{x \to \frac{5}{2}} 2$

Step 1.2

Evaluate the limit of $2$ which is constant as $x$ approaches $\frac{5}{2}$ .

$- lim_{x \to \frac{5}{2}} x + 2$

Step 2

Evaluate the limit of $x$ by plugging in $\frac{5}{2}$ for $x$ .

$- \frac{5}{2} + 2$

Step 3

Simplify the answer.

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Step 3.1

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

$- \frac{5}{2} + 2 \cdot \frac{2}{2}$

Step 3.2

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

$- \frac{5}{2} + \frac{2 \cdot 2}{2}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{- 5 + 2 \cdot 2}{2}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $2$ by $2$ .

$\frac{- 5 + 4}{2}$

Step 3.4.2

Add $- 5$ and $4$ .

$\frac{- 1}{2}$

Step 3.5

Move the negative in front of the fraction.

$- \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$