Calculus Examples

$\frac{lim_{x \to 3} \sqrt[3]{x} - \sqrt[3]{3}}{x - 3}$

Step 1

Evaluate the limit.

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Step 1.1

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

$\frac{lim_{x \to 3} \sqrt[3]{x} - lim_{x \to 3} \sqrt[3]{3}}{x - 3}$

Step 1.2

Move the limit under the radical sign.

$\frac{\sqrt[3]{lim_{x \to 3} x} - lim_{x \to 3} \sqrt[3]{3}}{x - 3}$

Step 1.3

Evaluate the limit of $\sqrt[3]{3}$ which is constant as $x$ approaches $3$ .

$\frac{\sqrt[3]{lim_{x \to 3} x} - \sqrt[3]{3}}{x - 3}$

Step 2

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

$\frac{\sqrt[3]{3} - \sqrt[3]{3}}{x - 3}$

Step 3

Simplify the answer.

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Step 3.1

Subtract $\sqrt[3]{3}$ from $\sqrt[3]{3}$ .

$\frac{0}{x - 3}$

Step 3.2

Divide $0$ by $x - 3$ .

$0$