Замечательные пределы: [latex] \lim_{n \to \infty} (1- \frac{2}{x})^{x} \lim_{n \to \infty} (1+ \frac{2}{3x})^{x}[/latex]

[latex] \lim_{x \to \infty}(1- \frac{2}{x})^x =\{1^{\infty}\}= \lim_{x \to \infty}(1+ \frac{-2}{x})^{ \frac{-2x}{-2} }=e^{-2}= \frac{1}{e^2} [/latex] [latex] \lim_{x \to \infty}(1+\frac{2}{3x})^x =\{1^{\infty}\}= \lim_{x \to \infty}(1+\frac{2}{3x})^{ \frac{3\cdot 2x}{2\cdot3} } =e^{ \frac{2}{3} }[/latex]