Calculus Examples

$\frac{lim_{x \to 16} 4 - \sqrt{x}}{x - 16}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $16$ .

$\frac{lim_{x \to 16} 4 - lim_{x \to 16} \sqrt{x}}{x - 16}$

Step 1.2

Evaluate the limit of $4$ which is constant as $x$ approaches $16$ .

$\frac{4 - lim_{x \to 16} \sqrt{x}}{x - 16}$

Step 1.3

Move the limit under the radical sign.

$\frac{4 - \sqrt{lim_{x \to 16} x}}{x - 16}$

Step 2

Evaluate the limit of $x$ by plugging in $16$ for $x$ .

$\frac{4 - \sqrt{16}}{x - 16}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

Rewrite $16$ as $4^{2}$ .

$\frac{4 - \sqrt{4^{2}}}{x - 16}$

Step 3.1.2

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

$\frac{4 - 1 \cdot 4}{x - 16}$

Step 3.1.3

Multiply $- 1$ by $4$ .

$\frac{4 - 4}{x - 16}$

Step 3.1.4

Subtract $4$ from $4$ .

$\frac{0}{x - 16}$

Step 3.2

Divide $0$ by $x - 16$ .

$0$