Calculus Examples

$lim_{x \to c} \sqrt{12 \cdot f (x)}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

$\sqrt{lim_{x \to c} 12 \cdot f (x)}$

Step 1.2

Move the term $12$ outside of the limit because it is constant with respect to $x$ .

$\sqrt{12 lim_{x \to c} f (x)}$

Step 2

Evaluate the limit of $f (x)$ by plugging in $c$ for $x$ .

$\sqrt{12 f (c)}$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $12 f (c)$ as $2^{2} \cdot (3 f (c))$ .

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Step 3.1.1

Factor $4$ out of $12$ .

$\sqrt{4 (3) f (c)}$

Step 3.1.2

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 3 f (c)}$

Step 3.1.3

Add parentheses.

$\sqrt{2^{2} \cdot (3 f (c))}$

Step 3.2

Pull terms out from under the radical.

$2 \sqrt{3 f (c)}$