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

题目

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

答案

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.