Question

lim[2-√(xy+4)]/xy x趋向于0 y趋向于0

Answer 1

lim[2-√(xy+4)]/xy

=lim[2-√(xy+4)][2+√(xy+4)]/{xy[2+√(xy+4)]}

=lim(x-->0,y---->0)(-xy)/[xy[2+√(xy+4)]]

=-lim(x-->0,y---->0)1/[2+√(xy+4)]

=-1/4