Question

Sobre propriedades e limites de funções

lim (1+3/x)×

x→∞

Answer 1

Resposta:

Explicação passo-a-passo:

Lembrete

$\lim_{x \to \infty}(1 + \frac{1}{x})^{x} =e\\\\\ \lim_{x \to \00}(1+x)^{\frac{1}{x}}=e\\\\ \lim_{x \to \infty}(1+\frac{3}{x})^{x}\\\\\frac{3}{x}=u;x-> oo =>u->0\\\\x.u=3=>x=\frac{3}{u}\\\\ \lim_{x \to \infty}(1+\frac{3}{x})^{x}= \lim_{x \to \00}(1+u)^{\frac{3}{u}}=\\\\ \lim_{x \to \00} [(1+u)^{\frac{1}{u}}]^{3}}=e^{3}$