Question

Помогите с пределами

Answer 1

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