Calculus Examples

$lim_{x \to {(- 2)}^{-}} \sqrt{- x - 2} + 4$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 2$ .

$lim_{x \to {(- 2)}^{-}} \sqrt{- x - 2} + lim_{x \to {(- 2)}^{-}} 4$

Step 2

Move the limit under the radical sign.

$\sqrt{lim_{x \to {(- 2)}^{-}} - x - 2} + lim_{x \to {(- 2)}^{-}} 4$

Step 3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 2$ .

$\sqrt{- lim_{x \to {(- 2)}^{-}} x - lim_{x \to {(- 2)}^{-}} 2} + lim_{x \to {(- 2)}^{-}} 4$

Step 4

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

$\sqrt{- lim_{x \to {(- 2)}^{-}} x - 1 \cdot 2} + lim_{x \to {(- 2)}^{-}} 4$

Step 5

Evaluate the limit of $4$ which is constant as $x$ approaches $- 2$ .

$\sqrt{- lim_{x \to {(- 2)}^{-}} x - 1 \cdot 2} + 4$

Step 6

Simplify terms.

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Step 6.1

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

$\sqrt{2 - 1 \cdot 2} + 4$

Step 6.2

Simplify the answer.

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Step 6.2.1

Simplify each term.

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Step 6.2.1.1

Multiply $- 1$ by $2$ .

$\sqrt{2 - 2} + 4$

Step 6.2.1.2

Subtract $2$ from $2$ .

$\sqrt{0} + 4$

Step 6.2.1.3

Rewrite $0$ as $0^{2}$ .

$\sqrt{0^{2}} + 4$

Step 6.2.1.4

Pull terms out from under the radical, assuming positive real numbers.

$0 + 4$

Step 6.2.2

Add $0$ and $4$ .

$4$