Calculus Examples

$lim_{x \to 4} x + \sqrt{x}$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4$ .

$lim_{x \to 4} x + lim_{x \to 4} \sqrt{x}$

Step 2

Move the limit under the radical sign.

$lim_{x \to 4} x + \sqrt{lim_{x \to 4} x}$

Step 3

Evaluate the limits by plugging in $4$ for all occurrences of $x$ .

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Step 3.1

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$4 + \sqrt{lim_{x \to 4} x}$

Step 3.2

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$4 + \sqrt{4}$

Step 4

Simplify the answer.

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Step 4.1

Simplify each term.

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Step 4.1.1

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

$4 + \sqrt{2^{2}}$

Step 4.1.2

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

$4 + 2$

Step 4.2

Add $4$ and $2$ .

$6$