x->0+,lim(1/X)^tanx=lim(1+(1-x)/x)^tanx=lim(1+(1-x)/x)^(x/(1-x)*(1-x)/x*tanx)
=lim e^((1-x)/x*tanx)=e^(lim(1-x)/x*tanx)=e^(lim(1-x))=e^1=e
x->0,设y=1/x->∞,不太清楚你表达式中e^(1/x)^2的具体形式,lim e^(y^2)/y^2（再替换一次z=y^2->∞）还是lim e^2y/(y^2),结果都是∞,e^x形式的增长速度还是太快了,无函数能及呀