Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

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

Step 2

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

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

Step 3

Simplify the answer.

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Step 3.1

Multiply $- 2$ by $2$ .

$\sqrt{4 - 4}$

Step 3.2

Subtract $4$ from $4$ .

$\sqrt{0}$

Step 3.3

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

$\sqrt{0^{2}}$

Step 3.4

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

$0$