Calculus Examples

$lim_{x \to 0} \sqrt{x + 1}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Move the limit under the radical sign.

$\sqrt{lim_{x \to 0} x + 1}$

Step 1.2

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

$\sqrt{lim_{x \to 0} x + lim_{x \to 0} 1}$

Step 1.3

Evaluate the limit of $1$ which is constant as $x$ approaches $0$ .

$\sqrt{lim_{x \to 0} x + 1}$

Step 2

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

$\sqrt{0 + 1}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Add $0$ and $1$ .

$\sqrt{1}$

Step 3.2

Any root of $1$ is $1$ .

$1$