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)
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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)
A.在(0,0)点连续,但偏导不存在
B.在(0,0)点可微
C.在(0,0)点偏导存在,但不连续
D.在(0,0)点偏导存在,但不可微
A.在(0,0)点连续,但偏导不存在
B.在(0,0)点可微
C.在(0,0)点偏导存在,但不连续
D.在(0,0)点偏导存在,但不可微
![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)](/uploads/image/z/5183724-12-4.jpg?t=g%EF%BC%88x%2Cy%EF%BC%89%3D%7Cx-y%7Cf%28x%2Cy%29%2Cf%28x%2Cy%29%E5%9C%A8%280%2C0%29%E7%82%B9%E8%BF%9E%E7%BB%AD%E4%B8%94f%EF%BC%880%2C0%EF%BC%89%3D0%2C%E5%88%99g%28x%2Cy%29)
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
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
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