Calculus Examples

$lim_{x \to 5} \sqrt{x - 1}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Move the limit under the radical sign.

$\sqrt{lim_{x \to 5} x - 1}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $5$ .

$\sqrt{lim_{x \to 5} x - lim_{x \to 5} 1}$

Step 1.3

Evaluate the limit of $1$ which is constant as $x$ approaches $5$ .

$\sqrt{lim_{x \to 5} x - 1 \cdot 1}$

Step 2

Evaluate the limit of $x$ by plugging in $5$ for $x$ .

$\sqrt{5 - 1 \cdot 1}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Multiply $- 1$ by $1$ .

$\sqrt{5 - 1}$

Step 3.2

Subtract $1$ from $5$ .

$\sqrt{4}$

Step 3.3

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

$\sqrt{2^{2}}$

Step 3.4

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

$2$