Question

lim x->0 под корнем1+x - корень1-x / x

Answer 1

$lim_{xto0}frac{sqrt{1+x}-sqrt{1-x}}{x}=lim_{xto0}frac{(sqrt{1+x}-sqrt{1-x})(sqrt{1+x}+sqrt{1-x})}{x*(sqrt{1+x}+sqrt{1-x})}=\=lim_{xto0}frac{(sqrt{1+x})^2-(sqrt{1-x})^2}{x(sqrt{1+x}+sqrt{1-x})}=lim_{xto0}frac{1+x-(1-x)}{x(sqrt{1+x}+sqrt{1-x})}=\=lim_{xto0}frac{2x}{x(sqrt{1+x}+sqrt{1-x})}=lim_{xto0}frac{2}{sqrt{1+x}+sqrt{1-x}}=\=frac{2}{sqrt{1+0}+sqrt{1-0}}=frac{2}{2}=1$