Question

как решить???
1)Lim (√x+2-√x-2) x ->∞
2)Lim( √x+2-√2-x / 3x ) x -> 0

Answer 1

$lim_{xto infty}(sqrt{x+2}-sqrt{x-2})=limfrac{(x+2)-(x-2)}{sqrt{x+2}+sqrt{x-2}}=\\=lim_{xto infty }frac{4}{sqrt{x+2}+sqrt{x-2}}=[frac{4}{infty}]=0\\\lim_{xto 0}frac{sqrt{x+2}-sqrt{x-2}}{3x}=lim_{xto 0}frac{(x+2)-(x-2)}{3x(sqrt{x+2}+sqrt{x-2})}=[frac{4}{0}]=infty$