求二元函数极限 x→0,y→0,lim [(x+y)sin(1/x)cos(1/y)]_数学解答

求二元函数极限 x→0,y→0,lim [(x+y)sin(1/x)cos(1/y)]

人气：483 ℃　时间：2019-09-30 19:21:13

解答

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