二元函数f(x,y)在点(0,0)处可微的一个充要条件是()
A.
lim |
(x,y)→(0,0)
[f(x,y)−f(0,0)]=0
B.
lim |
x→0
f(x,0)−f(0,0)
x |
=0,且
lim |
y→0
f(0,y)−f(0,0)
y |
=0
C.
lim |
(x,y)→(0,0)
f(x,y)−f(0,0)
|
x2+y2
=0
D.
lim |
x→0
[
f | ′
x
(x,0)−
f | ′
x
(0,0)]=0,且
lim |
y→0
[
lim |
x→0
1(0,y)−
lim |
x→0
1(0,0)]=0