求lim(x→0,y→0) ysin(1/xy)的极限

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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)

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