Calculus Examples

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

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 $- 2$ .

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

Step 1.2

Evaluate the limit of $2$ which is constant as $x$ approaches $- 2$ .

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

Step 2

Evaluate the limit of $x$ by plugging in $- 2$ for $x$ .

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

Step 3

Simplify the answer.

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Step 3.1

Cancel the common factor of $- 2 + 2$ and $2$ .

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Step 3.1.1

Factor $2$ out of $- 2$ .

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

Step 3.1.2

Factor $2$ out of $2$ .

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

Step 3.1.3

Factor $2$ out of $2 \cdot - 1 + 2 \cdot 1$ .

$\frac{2 \cdot (- 1 + 1)}{2}$

Step 3.1.4

Cancel the common factors.

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Step 3.1.4.1

Factor $2$ out of $2$ .

$\frac{2 \cdot (- 1 + 1)}{2 (1)}$

Step 3.1.4.2

Cancel the common factor.

$\frac{2 \cdot (- 1 + 1)}{2 \cdot 1}$

Step 3.1.4.3

Rewrite the expression.

$\frac{- 1 + 1}{1}$

Step 3.1.4.4

Divide $- 1 + 1$ by $1$ .

$- 1 + 1$

Step 3.2

Add $- 1$ and $1$ .

$0$