Calculus Examples

$lim_{x \to 8} (\sqrt[3]{x}) (x - 2)$

Step 1

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $8$ .

$lim_{x \to 8} \sqrt[3]{x} \cdot lim_{x \to 8} x - 2$

Step 2

Move the limit under the radical sign.

$\sqrt[3]{lim_{x \to 8} x} \cdot lim_{x \to 8} x - 2$

Step 3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $8$ .

$\sqrt[3]{lim_{x \to 8} x} \cdot (lim_{x \to 8} x - lim_{x \to 8} 2)$

Step 4

Evaluate the limit of $2$ which is constant as $x$ approaches $8$ .

$\sqrt[3]{lim_{x \to 8} x} \cdot (lim_{x \to 8} x - 1 \cdot 2)$

Step 5

Evaluate the limits by plugging in $8$ for all occurrences of $x$ .

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Step 5.1

Evaluate the limit of $x$ by plugging in $8$ for $x$ .

$\sqrt[3]{8} \cdot (lim_{x \to 8} x - 1 \cdot 2)$

Step 5.2

Evaluate the limit of $x$ by plugging in $8$ for $x$ .

$\sqrt[3]{8} \cdot (8 - 1 \cdot 2)$

Step 6

Simplify the answer.

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Step 6.1

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3}} \cdot (8 - 1 \cdot 2)$

Step 6.2

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

$2 \cdot (8 - 1 \cdot 2)$

Step 6.3

Multiply $- 1$ by $2$ .

$2 \cdot (8 - 2)$

Step 6.4

Subtract $2$ from $8$ .

$2 \cdot 6$

Step 6.5

Multiply $2$ by $6$ .

$12$