Calculus Examples

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

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 $0$ .

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

Step 1.2

Move the limit under the radical sign.

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

Step 1.3

Evaluate the limit of $3$ which is constant as $x$ approaches $0$ .

$\sqrt[3]{lim_{x \to 0} x} - 1 \cdot 3$

Step 2

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

$\sqrt[3]{0} - 1 \cdot 3$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

$\sqrt[3]{0^{3}} - 1 \cdot 3$

Step 3.1.2

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

$0 - 1 \cdot 3$

Step 3.1.3

Multiply $- 1$ by $3$ .

$0 - 3$

Step 3.2

Subtract $3$ from $0$ .

$- 3$