求lim(x→0,y→0) ysin(1/xy)的极限

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/27 23:03:14

求lim(x→0,y→0) ysin(1/xy)的极限
求lim(x→0,y→0) ysin(1/xy)的极限

求lim(x→0,y→0) ysin(1/xy)的极限
lim(x→0,y→0) ysin(1/xy)
=(lim(y→0) y)*lim(x→0,y→0) sin(1/xy)
由于lim(y→0) y=0,是无穷小量
|lim(x→0,y→0) sin(1/xy)|≤1,是有界量
根据无穷小量乘以有界量等于无穷小量知
lim(x→0,y→0) ysin(1/xy)=0

lim(x→0,y→0) ysin(1/xy)
=(lim(y→0) y)*lim(x→0,y→0) sin(1/xy)
由于lim(y→0) y=0,是无穷小量
|lim(x→0,y→0) sin(1/xy)|≤1,是有界量
根据无穷小量乘以有界量等于无穷小量知
lim(x→0,y→0) ysin(1/xy)=0