Precalculus Examples

$\frac{lim_{x \to 8} 6 x + 4}{x^{4}}$

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 $8$ .

$\frac{lim_{x \to 8} 6 x + lim_{x \to 8} 4}{x^{4}}$

Step 1.2

Move the term $6$ outside of the limit because it is constant with respect to $x$ .

$\frac{6 lim_{x \to 8} x + lim_{x \to 8} 4}{x^{4}}$

Step 1.3

Evaluate the limit of $4$ which is constant as $x$ approaches $8$ .

$\frac{6 lim_{x \to 8} x + 4}{x^{4}}$

Step 2

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

$\frac{6 \cdot 8 + 4}{x^{4}}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $6$ by $8$ .

$\frac{48 + 4}{x^{4}}$

Step 3.2

Add $48$ and $4$ .

$\frac{52}{x^{4}}$