Vamos usar um dos Limites fundamentais :
[tex]\displaystyle \lim_{\displaystyle \text x\to \infty}(\ 1+\frac{\text k}{\text x}\ )^{\text x} = \text e^{\text k}[/tex]
item a)
[tex]\displaystyle \lim_{\displaystyle \text x\to\infty}(1+\frac{1}{\text x})^{2\text x} \\\\\\ \displaystyle [\lim_{\displaystyle \text x\to\infty}(1+\frac{1}{\text x})^{\text x}]^2 = \text e^2 \\\\\\\ \underline{\text{Portanto} }: \\\\ \huge\boxed{\lim_{\displaystyle \text x\to\infty}(1+\frac{1}{\text x})^{2\text x} = \text e^2\ }\checkmark[/tex]
item b)
[tex]\huge\boxed{\displaystyle \lim_{\displaystyle \text x\to\infty}(1+\frac{3}{\text x})^{\text x} = \text e^3\ }\checkmark[/tex]
