Calculus Examples

$lim_{x \to 4} \sqrt{x^{2} - 7}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

$\sqrt{lim_{x \to 4} x^{2} - 7}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4$ .

$\sqrt{lim_{x \to 4} x^{2} - lim_{x \to 4} 7}$

Step 1.3

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

$\sqrt{{(lim_{x \to 4} x)}^{2} - lim_{x \to 4} 7}$

Step 1.4

Evaluate the limit of $7$ which is constant as $x$ approaches $4$ .

$\sqrt{{(lim_{x \to 4} x)}^{2} - 1 \cdot 7}$

Step 2

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$\sqrt{4^{2} - 1 \cdot 7}$

Step 3

Simplify the answer.

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Step 3.1

Raise $4$ to the power of $2$ .

$\sqrt{16 - 1 \cdot 7}$

Step 3.2

Multiply $- 1$ by $7$ .

$\sqrt{16 - 7}$

Step 3.3

Subtract $7$ from $16$ .

$\sqrt{9}$

Step 3.4

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2}}$

Step 3.5

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

$3$