limg(x,y)=lim|x-y|*f(0,0)=0 =g(0,0) (x到0,y到0)
即连续C错
gx(0,0)=lim(g(x,0)-g(0,0))/x
=lim|x|f(x,0)/x
=f(0,0)lim|x|/x
=0
即偏导数存在
所以A错
lim(Δg-dg)/ρ=lim(|x-y|f(x,y))/√(x^2+y^2)
0<=(|x-y||f(x,y)|)/√(x^2+y^2)<=|f(x,y)|
limf(x,y)=0
夹逼准则得lim(Δg-dg)/ρ=0
所以可微B对
选B