Question

Calcule os limites, utilizando o primeiro e o segundo limite fundamental:
$\lim_{x \to +\infty}(\frac{x+3}{x+2} )^{x+2}$

Answer 1

$\displaystyle \sf \text{Limite fundamental :}\\\\ \lim_{x\to \pm\infty} \left(1+\frac{1}{x}\right)^{x}= e \\\\\\ temos : \\\\ \lim_{x\to +\infty} \left(\frac{x+3}{x+2} \right)^{x+2} \\\\\\ \lim_{x\to +\infty} \left(\frac{x+2}{x+2} +\frac{1}{x+2}\right)^{x+2} \\\\\\ \huge\boxed{\sf \lim_{x\to +\infty} \left(1 +\frac{1}{x+2}\right)^{x+2} =e \ }\checkmark$