lim(x→0)(1-2x)^(1/(-2x))=e,所以 lim(x→0)(1-2x)^(1/x)=e^(-2),lim(x→0)(1+3x)^(1/(3x))=e,所以lim(x→0)(1+3x)^(1/x)=e^3,因此,lim(x→0)((1-2x)/(1+3x)) ^(1/x)=e^(-5).