Question

evaluate the limit

\\\lim_{x \to \infty} \frac{5 + 10x}{4 - 6x}\\

Explanation:

Divide numerator and denominator by the highest power of x

$$ \lim_{x \to \infty} \frac{5 + 10x}{4 - 6x} = \lim_{x \to \infty} \frac{\frac{5}{x} + 10}{\frac{4}{x} - 6} $$

Evaluate the limit of each term as x approaches infinity

$$ \lim_{x \to \infty} \frac{5}{x} = 0,\quad \lim_{x \to \infty} \frac{4}{x} = 0 $$

Simplify the expression to find the final limit

$$ \frac{0 + 10}{0 - 6} = -\frac{10}{6} = -\frac{5}{3} $$

Answer:

Evaluate the limit

\(\lim_{x \to \infty} \frac{5 + 10x}{4 - 6x} =\) <blank>\(-\frac{5}{3}\)</blank>