Precalculus Examples

$lim_{x \to 8} 5 - 3 x - 8 x^{3}$

Step 1

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

$lim_{x \to 8} 5 - lim_{x \to 8} 3 x - lim_{x \to 8} 8 x^{3}$

Step 2

Evaluate the limit of $5$ which is constant as $x$ approaches $8$ .

$5 - lim_{x \to 8} 3 x - lim_{x \to 8} 8 x^{3}$

Step 3

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$5 - 3 lim_{x \to 8} x - lim_{x \to 8} 8 x^{3}$

Step 4

Move the term $8$ outside of the limit because it is constant with respect to $x$ .

$5 - 3 lim_{x \to 8} x - 8 lim_{x \to 8} x^{3}$

Step 5

Move the exponent $3$ from $x^{3}$ outside the limit using the Limits Power Rule.

$5 - 3 lim_{x \to 8} x - 8 {(lim_{x \to 8} x)}^{3}$

Step 6

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

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Step 6.1

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

$5 - 3 \cdot 8 - 8 {(lim_{x \to 8} x)}^{3}$

Step 6.2

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

$5 - 3 \cdot 8 - 8 \cdot 8^{3}$

Step 7

Simplify the answer.

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Step 7.1

Simplify each term.

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Step 7.1.1

Multiply $- 3$ by $8$ .

$5 - 24 - 8 \cdot 8^{3}$

Step 7.1.2

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

$5 - 24 - 8 \cdot 512$

Step 7.1.3

Multiply $- 8$ by $512$ .

$5 - 24 - 4096$

Step 7.2

Subtract $24$ from $5$ .

$- 19 - 4096$

Step 7.3

Subtract $4096$ from $- 19$ .

$- 4115$