Question

g（x,y）=|x-y|f(x,y),f(x,y)在(0,0)点连续且f（0,0）=0,则g(x,y)

Answer 1

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