Question

lim 3-2x/5x+1 para x-> + infinito

Answer 1

Oi :)
$\lim_{x \to +\infty} \frac{3-2x}{5x+1} \\ \\ \lim_{x \to +\infty} \frac{x( \frac{3}{x} -2)}{x(5+ \frac{1}{x}) } \ \ \ colocando \ x \ em \ evide^encia \\ \\ \lim_{x \to +\infty} \frac{ \frac{3}{x} -2}{5+ \frac{1}{x} } \\ \\ \lim_{x \to +\infty} \frac{ \frac{3}{\infty} -2}{5+ \frac{1}{\infty} } \\ \\ \lim_{x \to +\infty} \frac{0-2}{5+0 } \\ \\ \lim_{x \to +\infty} -\frac{2}{5} \\ \\ \\ \\ \boxed{ \lim_{x \to +\infty} \frac{3-2x}{5x+1}=-\frac{2}{5} }$