Calculus Examples

$lim_{x \to 8} (1 + \sqrt[3]{8}) (2 - 6 {(8)}^{2} + 8^{3})$

Step 1

Evaluate the limit of $(1 + \sqrt[3]{8}) (2 - 6 {(8)}^{2} + 8^{3})$ which is constant as $x$ approaches $8$ .

$(1 + \sqrt[3]{8}) (2 - 6 {(8)}^{2} + 8^{3})$

Step 2

Simplify the answer.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$(1 + \sqrt[3]{2^{3}}) (2 - 6 {(8)}^{2} + 8^{3})$

Step 2.1.2

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

$(1 + 2) (2 - 6 {(8)}^{2} + 8^{3})$

Step 2.2

Add $1$ and $2$ .

$3 (2 - 6 {(8)}^{2} + 8^{3})$

Step 2.3

Simplify each term.

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Step 2.3.1

Raise $8$ to the power of $2$ .

$3 (2 - 6 \cdot 64 + 8^{3})$

Step 2.3.2

Multiply $- 6$ by $64$ .

$3 (2 - 384 + 8^{3})$

Step 2.3.3

Raise $8$ to the power of $3$ .

$3 (2 - 384 + 512)$

Step 2.4

Subtract $384$ from $2$ .

$3 (- 382 + 512)$

Step 2.5

Add $- 382$ and $512$ .

$3 \cdot 130$

Step 2.6

Multiply $3$ by $130$ .

$390$