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

Question

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

Answer 1

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.