Calculus Examples

$lim_{x \to 1} \sqrt{5 x + 4}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

$\sqrt{lim_{x \to 1} 5 x + 4}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$\sqrt{lim_{x \to 1} 5 x + lim_{x \to 1} 4}$

Step 1.3

Move the term $5$ outside of the limit because it is constant with respect to $x$ .

$\sqrt{5 lim_{x \to 1} x + lim_{x \to 1} 4}$

Step 1.4

Evaluate the limit of $4$ which is constant as $x$ approaches $1$ .

$\sqrt{5 lim_{x \to 1} x + 4}$

Step 2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$\sqrt{5 \cdot 1 + 4}$

Step 3

Simplify the answer.

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Step 3.1

Multiply $5$ by $1$ .

$\sqrt{5 + 4}$

Step 3.2

Add $5$ and $4$ .

$\sqrt{9}$

Step 3.3

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2}}$

Step 3.4

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

$3$