Calculus Examples

$lim_{x \to 2} \sqrt[3]{12 x + 3}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Move the limit under the radical sign.

$\sqrt[3]{lim_{x \to 2} 12 x + 3}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

$\sqrt[3]{lim_{x \to 2} 12 x + lim_{x \to 2} 3}$

Step 1.3

Move the term $12$ outside of the limit because it is constant with respect to $x$ .

$\sqrt[3]{12 lim_{x \to 2} x + lim_{x \to 2} 3}$

Step 1.4

Evaluate the limit of $3$ which is constant as $x$ approaches $2$ .

$\sqrt[3]{12 lim_{x \to 2} x + 3}$

Step 2

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$\sqrt[3]{12 \cdot 2 + 3}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Multiply $12$ by $2$ .

$\sqrt[3]{24 + 3}$

Step 3.2

Add $24$ and $3$ .

$\sqrt[3]{27}$

Step 3.3

Rewrite $27$ as $3^{3}$ .

$\sqrt[3]{3^{3}}$

Step 3.4

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

$3$