Calculus Examples

$\frac{lim_{x \to 144} \sqrt{x} - 12}{x - 144}$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $144$ .

$\frac{lim_{x \to 144} \sqrt{x} - lim_{x \to 144} 12}{x - 144}$

Step 1.2

Move the limit under the radical sign.

$\frac{\sqrt{lim_{x \to 144} x} - lim_{x \to 144} 12}{x - 144}$

Step 1.3

Evaluate the limit of $12$ which is constant as $x$ approaches $144$ .

$\frac{\sqrt{lim_{x \to 144} x} - 1 \cdot 12}{x - 144}$

Step 2

Evaluate the limit of $x$ by plugging in $144$ for $x$ .

$\frac{\sqrt{144} - 1 \cdot 12}{x - 144}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

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

$\frac{\sqrt{12^{2}} - 1 \cdot 12}{x - 144}$

Step 3.1.2

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

$\frac{12 - 1 \cdot 12}{x - 144}$

Step 3.1.3

Multiply $- 1$ by $12$ .

$\frac{12 - 12}{x - 144}$

Step 3.1.4

Subtract $12$ from $12$ .

$\frac{0}{x - 144}$

Step 3.2

Divide $0$ by $x - 144$ .

$0$