函数f(x,y)在点O(0,0)处______,麻烦对每个选项单独分析一下。

填【A】【1】∵ |sin[1/(x²+y²)]|≤1∴ lim{(x²+y²)sin[1/(x²+y²)]}≤lim(x²+y²)=0∴ lim f(x，y)=0=f(0，0) x→0 y→0排除B选项【2】∂f/∂x=2x{cos[1/(x²+y²)]*[-2x/(x²+y²)²]=[-4x²/(x²+y²)²]cos[1/(x²+y²)²]偏导数在(0，0)处不存在