x→0lim (arctanx/x)^(1/x^2)=lim e^ln (arctanx/x)^(1/x^2)=e^lim ln (arctanx/x)^(1/x^2)考虑lim ln (arctanx/x)^(1/x^2)=lim ln(arctanx/x) / x^2=lim ln(1+arctanx/x-1) / x^2根据等价无穷小：ln(1+x)~x=lim (ar...