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lim(x->0,y->0)f(x,y)=0=f(0,0),所以：在点（0,0）连续
fx(0,0)=lim(x->0){[x 2×sin(1/x 2)]-f(0,0)}/x
=lim(x->0)x×sin(1/x 2)=0
fy(0,0)=lim(y->0){[y 2×sin(1/y 2)]-f(0,0)}/y
=lim(y->0)y×sin(1/y 2)=0
fx(0,0)=lim(x->0){[x 2×sin(1/x 2)]-f(0,0)}/x
=lim(x->0)x×sin(1/x 2)=0
fy(0,0)=lim(y->0){[y 2×sin(1/y 2)]-f(0,0)}/y
=lim(y->0)y×sin(1/y 2)=0
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你好！
解：∵im(x->0,y->0)f(x,y)=0=f(0,0) ∴在点（0,0）连续
fx(0,0)=lim(x->0){[x 2×sin(1/x 2)]-f(0,0)}/x
=lim(x->0)x×sin(1/x 2)=0
fy(0,0)=lim(y->0){[y 2×sin(1/y 2)]-f(0,0)}/y
=lim(y->0)y×sin(1/y 2)=0
望采纳哦！O(∩_∩)O谢谢
解：∵im(x->0,y->0)f(x,y)=0=f(0,0) ∴在点（0,0）连续
fx(0,0)=lim(x->0){[x 2×sin(1/x 2)]-f(0,0)}/x
=lim(x->0)x×sin(1/x 2)=0
fy(0,0)=lim(y->0){[y 2×sin(1/y 2)]-f(0,0)}/y
=lim(y->0)y×sin(1/y 2)=0
望采纳哦！O(∩_∩)O谢谢
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