Lim x- больше 0 под корнем1+x - корень1-x / x

[latex]lim_{x\to0}\frac{\sqrt{1+x}-\sqrt{1-x}}{x}=lim_{x\to0}\frac{(\sqrt{1+x}-\sqrt{1-x})(\sqrt{1+x}+\sqrt{1-x})}{x*(\sqrt{1+x}+\sqrt{1-x})}=\\=lim_{x\to0}\frac{(\sqrt{1+x})^2-(\sqrt{1-x})^2}{x(\sqrt{1+x}+\sqrt{1-x})}=lim_{x\to0}\frac{1+x-(1-x)}{x(\sqrt{1+x}+\sqrt{1-x})}=\\=lim_{x\to0}\frac{2x}{x(\sqrt{1+x}+\sqrt{1-x})}=lim_{x\to0}\frac{2}{\sqrt{1+x}+\sqrt{1-x}}=\\=\frac{2}{\sqrt{1+0}+\sqrt{1-0}}=\frac{2}{2}=1[/latex]