Calculus Examples

$lim_{x \to 0} \sqrt{64 + x^{2}}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

$\sqrt{lim_{x \to 0} 64 + x^{2}}$

Step 1.2

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

$\sqrt{lim_{x \to 0} 64 + lim_{x \to 0} x^{2}}$

Step 1.3

Evaluate the limit of $64$ which is constant as $x$ approaches $0$ .

$\sqrt{64 + lim_{x \to 0} x^{2}}$

Step 1.4

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

$\sqrt{64 + {(lim_{x \to 0} x)}^{2}}$

Step 2

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

$\sqrt{64 + 0^{2}}$

Step 3

Simplify the answer.

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Step 3.1

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

$\sqrt{64 + 0}$

Step 3.2

Add $64$ and $0$ .

$\sqrt{64}$

Step 3.3

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2}}$

Step 3.4

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

$8$