Question

помогите с пределами

Answer 1

$1)lim_{xto +infty }(x-sqrt{1+x+x^2})=limfrac{x^2-(1+x+x^2)}{x+sqrt{1+x+x^2}}=\\=limfrac{-1-x}{x+sqrt{}1+x+x^2}}=lim_{xto +infty}frac{frac{-1}{x}-1}{1+sqrt{frac{1}{x^2}+frac{1}{x}+1}}=frac{0-1}{1+1}=-frac{1}{2}\\2)lim_{xto 1}frac{sqrt{x}-1}{x-1}=limfrac{sqrt{x}-1}{(sqrt{x}-1)(sqrt{x}+1)}=lim_{xto 1} frac{1}{sqrt{x}+1}}=frac{1}{1+1}=frac{1}{2}$