lim sin(y×x^2+y^4)/(x^2+y^2) x,y都趋于0，

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limsin(y×x^2+y^4)/(x^2+y^2)x,y都趋于0，limsin(y×x^2+y^4)/(x^2+y^2)x,y都趋于0，limsin(y×x^2+y^4)/(x^2+y^2)x,y

lim sin(y×x^2+y^4)/(x^2+y^2) x,y都趋于0，
lim sin(y×x^2+y^4)/(x^2+y^2) x,y都趋于0，

lim sin(y×x^2+y^4)/(x^2+y^2) x,y都趋于0，
令y=kx
则lim sin(y×x^2+y^4)/(x^2+y^2)
=lim sin[ kx^3+(kx)^4 ]/[ (1+k^2)*x^2 ]
分子用等价无穷小替换
=lim [ k+(k^4)*x ]*(x^3)/[ (1+k^2)*x^2 ]
=lim [ k+(k^4)*x ]*x/(1+k^2)
=0