Calculus Examples

$lim_{x \to 0} x \sqrt[3]{x}$

Step 1

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $0$ .

$lim_{x \to 0} x \cdot lim_{x \to 0} \sqrt[3]{x}$

Step 2

Move the limit under the radical sign.

$lim_{x \to 0} x \cdot \sqrt[3]{lim_{x \to 0} x}$

Step 3

Evaluate the limits by plugging in $0$ for all occurrences of $x$ .

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Step 3.1

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$0 \cdot \sqrt[3]{lim_{x \to 0} x}$

Step 3.2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$0 \cdot \sqrt[3]{0}$

Step 4

Simplify the answer.

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Step 4.1

Rewrite $0$ as $0^{3}$ .

$0 \cdot \sqrt[3]{0^{3}}$

Step 4.2

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

$0 \cdot 0$

Step 4.3

Multiply $0$ by $0$ .

$0$