lim(x→+∞ )√x[√(x+2)-√x]
=lim(x→+∞ )√x[√(x+2)-√x][√(x+2)+√x]/[√(x+2)+√x]
=lim(x→+∞ )2√x/[√(x+2)+√x]
=lim(x→+∞ )2/[√(1+2/x)+1]
=1