Calculus Examples

$lim_{x \to 0} \sqrt{6 (x^{2} + 24)}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

$\sqrt{lim_{x \to 0} 6 (x^{2} + 24)}$

Step 1.2

Move the term $6$ outside of the limit because it is constant with respect to $x$ .

$\sqrt{6 lim_{x \to 0} x^{2} + 24}$

Step 1.3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $0$ .

$\sqrt{6 (lim_{x \to 0} x^{2} + lim_{x \to 0} 24)}$

Step 1.4

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

$\sqrt{6 ({(lim_{x \to 0} x)}^{2} + lim_{x \to 0} 24)}$

Step 1.5

Evaluate the limit of $24$ which is constant as $x$ approaches $0$ .

$\sqrt{6 ({(lim_{x \to 0} x)}^{2} + 24)}$

Step 2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$\sqrt{6 (0^{2} + 24)}$

Step 3

Simplify the answer.

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Step 3.1

Raising $0$ to any positive power yields $0$ .

$\sqrt{6 (0 + 24)}$

Step 3.2

Add $0$ and $24$ .

$\sqrt{6 \cdot 24}$

Step 3.3

Multiply $6$ by $24$ .

$\sqrt{144}$

Step 3.4

Rewrite $144$ as $12^{2}$ .

$\sqrt{12^{2}}$

Step 3.5

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

$12$