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)]

f(x,y) = (x+y)sin(1/x)cos(1/y)
0 ≤ | f(x,y)| ≤ |x+y| ≤ |x| + |y| -> 0
原式 = 0