Question

calcule o limite $\lim_{y \to \infty} ( \frac{2-3 y^{2} }{5 y^{2} +4y} )$ ??

a)  $- \frac{3}{5}$
b)  $\frac{3}{5}$
c)  $\frac{2}{5}$
d)   2

Answer 1

$\displaystyle \lim_{y \to +\infty} \frac{2-3y^{2}}{5y^{2}+4y} \\ \\ \\ \displaystyle \lim_{y \to +\infty} \frac{y^{2} \cdot (\displaystyle \frac{2}{y^{2}}-3)}{y^{2} \cdot (5+ \displaystyle \frac{4}{y} )} \\ \\ \\ \displaystyle \lim_{y \to +\infty} -\frac{3y^{2}}{5y^{2}} = \boxed{\boxed{- \frac{3}{5} }}$