Question

evaluate the limit

\\\lim_{x \to \infty} \frac{\sqrt{8 + 3x^2}}{8 + 5x}\\

Explanation:

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

$$ \lim_{x\to\infty} \frac{\sqrt{8 + 3x^2}}{8 + 5x} = \lim_{x\to\infty} \frac{\frac{\sqrt{8 + 3x^2}}{x}}{\frac{8 + 5x}{x}} $$

Simplify the algebraic expression for positive x

$$ \lim_{x\to\infty} \frac{\sqrt{\frac{8}{x^2} + 3}}{\frac{8}{x} + 5} $$

Evaluate the limit as x approaches infinity

$$ \frac{\sqrt{0 + 3}}{0 + 5} = \frac{\sqrt{3}}{5} $$

Answer:

Evaluate the limit

\(\lim_{x\to\infty} \frac{\sqrt{8 + 3x^2}}{8 + 5x} =\) <blank>\(\frac{\sqrt{3}}{5}\)</blank>