Question

evaluate the limit

\\\lim_{x \to \infty} \frac{10x + 10}{3x^2 - 10x + 4}\\

Explanation:

Divide numerator and denominator by the highest power of x

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

Simplify the rational expression

$$ \lim_{x \to +\infty} \frac{\frac{10}{x} + \frac{10}{x^2}}{3 - \frac{10}{x} + \frac{4}{x^2}} $$

Evaluate the limit as x approaches infinity

$$ \frac{0 + 0}{3 - 0 + 0} = \frac{0}{3} = 0 $$

Answer:

Evaluate the limit

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

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