Calculus Examples

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

Step 1

Move the limit under the radical sign.

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

Step 2

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

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

Step 3

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

$\sqrt[3]{- lim_{x \to 3} x - 1 \cdot 2}$

Step 4

Simplify terms.

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Step 4.1

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

$\sqrt[3]{- 3 - 1 \cdot 2}$

Step 4.2

Simplify the answer.

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Step 4.2.1

Multiply $- 1$ by $2$ .

$\sqrt[3]{- 3 - 2}$

Step 4.2.2

Subtract $2$ from $- 3$ .

$\sqrt[3]{- 5}$

Step 4.2.3

Rewrite $- 5$ as ${(- 1)}^{3} \cdot 5$ .

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Step 4.2.3.1

Rewrite $- 5$ as $- 1 (5)$ .

$\sqrt[3]{- 1 (5)}$

Step 4.2.3.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$\sqrt[3]{{(- 1)}^{3} \cdot 5}$

Step 4.2.4

Pull terms out from under the radical.

$- 1 \sqrt[3]{5}$

Step 4.2.5

Rewrite $- 1 \sqrt[3]{5}$ as $- \sqrt[3]{5}$ .

$- \sqrt[3]{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \sqrt[3]{5}$

Decimal Form:

$- 1.70997594 \dots$