Question

evaluate the limit

\\\lim_{x \to \infty} \frac{10x^2 - 10x + 9}{11x + 10}\\

Explanation:

Divide numerator and denominator by the highest power of x in the denominator

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

Simplify the rational expression

$$ \lim_{x \to \infty} \frac{10x - 10 + \frac{9}{x}}{11 + \frac{10}{x}} $$

Evaluate the limit as x approaches infinity

$$ \frac{\lim_{x \to \infty} (10x - 10 + 0)}{11 + 0} = \infty $$

Answer:

Evaluate the limit

$$ \lim_{x\to\infty} \frac{10x^2 - 10x + 9}{11x + 10} $$

<blank>\(\infty\)</blank>