求极限lim(xy)^2/(x^2+y^2)^2,(x,y)趋于(0,0)
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求极限lim(xy)^2/(x^2+y^2)^2,(x,y)趋于(0,0)求极限lim(xy)^2/(x^2+y^2)^2,(x,y)趋于(0,0)求极限lim(xy)^2/(x^2+y^2)^2,(
求极限lim(xy)^2/(x^2+y^2)^2,(x,y)趋于(0,0)
求极限lim(xy)^2/(x^2+y^2)^2,(x,y)趋于(0,0)
求极限lim(xy)^2/(x^2+y^2)^2,(x,y)趋于(0,0)
lim[x=y,x-->0](xy)^2/(x^2+y^2)^2
=lim[x=y,x-->0]x^4/(4x^4)
=1/4
lim[y=2x,x-->0](xy)^2/(x^2+y^2)^2
=lim[y=2x,x-->0]4x^4/(25x^4)
=4/25
二者不相等
所以极限不存在
lim
=lim
因为lim
lim
故lim
有lim
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