Question

Cálculo. Questão de limite com a resposta mais detalhada possível por favor.

Answer 1

$\lim_{y \to \infty} \frac{2^{y}+2^{2y}}{4+4^{y}} \\\\ \lim_{y \to \infty} \frac{(2^{y}+2^{2y})(\frac{1}{2^{2y}})}{(4+4^{y})(\frac{1}{2^{2y}})} \\\\ \lim_{y \to \infty} \frac{\frac{2^{y}}{2^{2y}}+\frac{2^{2y}}{2^{2y}}}{\frac{2^{2}}{2^{2y}}\frac{2^{2y}}{2^{2y}}} \\\\ \lim_{y \to \infty} \frac{1+2^{-y}}{1+2^{2-2y}} \\\\ \lim_{y \to \infty} \frac{1+\frac{1}{2^{y}}}{1+\frac{2^{2}}{2^{2y}}}} \\\\ \lim_{y \to \infty} \frac{1+\frac{1}{2^{ \infty}}}{1+\frac{2^{2}}{2 ^{\infty}}}}$

$\lim_{y \to \infty} \frac{1+0{}}{1+0}}} \to \boxed{1}$

Até mais !