Question

lim sin(y×x^2+y^4)/(x^2+y^2) x,y都趋于0，

Answer 1

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