Calculus Examples

$lim_{x \to 3} \sqrt{x + 1}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

$\sqrt{lim_{x \to 3} x + 1}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $3$ .

$\sqrt{lim_{x \to 3} x + lim_{x \to 3} 1}$

Step 1.3

Evaluate the limit of $1$ which is constant as $x$ approaches $3$ .

$\sqrt{lim_{x \to 3} x + 1}$

Step 2

Evaluate the limit of $x$ by plugging in $3$ for $x$ .

$\sqrt{3 + 1}$

Step 3

Simplify the answer.

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Step 3.1

Add $3$ and $1$ .

$\sqrt{4}$

Step 3.2

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

$\sqrt{2^{2}}$

Step 3.3

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

$2$