Question

lim->0 x/√(5-x)-√(5+x) найти предел

Answer 1

$displaystylelim_{xto0}frac x{sqrt{5-x}-sqrt{5+x}}=lim_{xto0}frac{x(sqrt{5-x}+sqrt{5+x})}{(5-x)-(5+x)}=\=lim_{xto0}frac{x(sqrt{5-x}+sqrt{5+x})}{-2x}=-frac12lim_{xto0}(sqrt{5-x}+sqrt{5+x})=\=-frac12(sqrt{5-0}+sqrt{5+0})=-sqrt5$