lim xy x趋近于0 —————— y趋近于0 根号下xy+4-2 求值 -2在根号外xy/ 根号下xy+4-2求值 -2在根_数学解答

lim xy x趋近于0 —————— y趋近于0 根号下xy+4-2 求值 -2在根号外
xy/ 根号下xy+4-2
求值 -2在根号外

人气：439 ℃　时间：2020-05-13 14:52:18

解答

lim(x->0,y->0){xy/[√(xy+4)-2]}=lim(x->0,y->0){xy[√(xy+4)+2]/[(xy+4)-4]}
(分子分母同乘√(xy+4)+2)
=lim(x->0,y->0){xy[√(xy+4)+2]/(xy)}
=lim(x->0,y->0)[√(xy+4)+2]
=√(0*0+4)+2
=4.