lim(x,y)趋近于(0,0)(xy^2-sinxy^2)/(x^3*y^6)=

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lim(x,y)趋近于(0,0)(xy^2-sinxy^2)/(x^3*y^6)=lim(x,y)趋近于(0,0)(xy^2-sinxy^2)/(x^3*y^6)=lim(x,y)趋近于(0,0)(x

lim(x,y)趋近于(0,0)(xy^2-sinxy^2)/(x^3*y^6)=
lim(x,y)趋近于(0,0)(xy^2-sinxy^2)/(x^3*y^6)=

lim(x,y)趋近于(0,0)(xy^2-sinxy^2)/(x^3*y^6)=
单变元时有lim (x-sinx)/x^3=lim (1-cosx)/3x^2=lim sinx/6x=1/6,
因此当x,y趋于0,0时,xy^2趋于0,故
lim (xy^2-sinxy^2)/(xy^2)^3=1/6.