Question

evaluate the limit

\\\lim_{x \to \infty} \frac{10x^3 - 11x^2 - 8x}{4 - 10x - 9x^3}\\

Explanation:

Identify the limit expression

Using the Limits at Infinity and Rational Function Limits knowledge points

$$ L = \lim_{x\to\infty} \frac{10x^3 - 11x^2 - 8x}{4 - 10x - 9x^3} $$

Divide numerator and denominator by the highest power

Using the Rational Function Limits knowledge point

$$ L = \lim_{x\to\infty} \frac{\frac{10x^3}{x^3} - \frac{11x^2}{x^3} - \frac{8x}{x^3}}{\frac{4}{x^3} - \frac{10x}{x^3} - \frac{9x^3}{x^3}} = \lim_{x\to\infty} \frac{10 - \frac{11}{x} - \frac{8}{x^2}}{\frac{4}{x^3} - \frac{10}{x^2} - 9} $$

Evaluate the limit of each term

Using the Limits at Infinity knowledge point

$$ L = \frac{10 - 0 - 0}{0 - 0 - 9} = -\frac{10}{9} $$

Answer:

Evaluate the limit

$$ \lim_{x\to\infty} \frac{10x^3 - 11x^2 - 8x}{4 - 10x - 9x^3} = $$

<blank>\(-\frac{10}{9}\)</blank>