Question

Найти предел.
limx→∞(x/(x+1))^2x-3

Answer 1

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