二元函数 $f(x, y)$ 在点 $(0,0)$ 处可微的一个充分条件是
A
$\lim _{(x, y) \rightarrow(0.0)}[f(x, y)-f(0,0)]=0$ ．
B
$\lim _{x \rightarrow 0} \frac{f(x, 0)-f(0,0)}{x}=0$ 且 $\lim _{y \rightarrow 0} \frac{f(0, y)-f(0,0)}{y}=0$ ．
C
$\lim _{(x, y) \rightarrow(0,0)} \frac{f(x, y)-f(0,0)}{\sqrt{x^2+y^2}}=0$ ．
D
$\lim _{x \rightarrow 0}\left[f_x^{\prime}(x, 0)-f_x^{\prime}(0,0)\right]=0$ 且 $\lim _{y \rightarrow 0}\left[f_y^{\prime}(0, y)-f_y^{\prime}(0,0)\right]=0$
E
F