Question

Замечательные пределы:
$lim_{n to infty} (1- frac{2}{x})^{x} lim_{n to infty} (1+ frac{2}{3x})^{x}$

Answer 1

$lim_{x to infty}(1- frac{2}{x})^x ={1^{infty}}= lim_{x to infty}(1+ frac{-2}{x})^{ frac{-2x}{-2} }=e^{-2}= frac{1}{e^2}$

$lim_{x to infty}(1+frac{2}{3x})^x ={1^{infty}}= lim_{x to infty}(1+frac{2}{3x})^{ frac{3cdot 2x}{2cdot3} } =e^{ frac{2}{3} }$