求(1+xy)^[1/(x+y)] 极限

题目

求(1+xy)^[1/(x+y)] 极限
求(1+xy)^[1/(x+y)] 的极限 x趋向于0 y趋向于0

答案

当x,y均趋于0时,
(1+xy)^[1/(x+y)]
=（1+xy)^{(1/xy)*[(xy)/(x+y)]}
=e^[1/(1/x+1/y)]
=e^0
=1