Question

lim (x стремится к 1) √x -√2-x/ x-1

Answer 1

$lim_{xto 1}, frac{sqrt{x}-sqrt{2-x}}{x-1}=lim_{xto 1}, frac{x-(2-x)}{(x-1)(sqrt{x}+sqrt{2-x})}=\\=lim_{xto 1}, frac{2(x-1)}{(x-1)(sqrt{x}+sqrt{2-x})}=lim_{xto 1}, frac{2}{sqrt{x}+sqrt{2-x}}=frac{2}{1+1}=1$