求二元函数极限 x→0,y→0,lim [(x+y)sin(1/x)cos(1/y)]
问题描述：
求二元函数极限 x→0,y→0,lim [(x+y)sin(1/x)cos(1/y)]
答
∵-(x+y)≤(x+y)sin(1/x)cos(1/y)≤x+y
又lim(x->0,y->0)(x+y)=0
∴根据夹逼定理知lim(x->0,y->0)[(x+y)sin(1/x)cos(1/y)]=0
答
(x+y)→0，
sin(1/x)有界
cos(1/y)有界
则此极限=0
答
f(x,y) = (x+y)sin(1/x)cos(1/y)
0 ≤ | f(x,y)| ≤ |x+y| ≤ |x| + |y| -> 0
原式 = 0