lim_{x->1}x^[1/(x-1)]
=lim_{x->1}(1+x-1)^[1/(x-1)]
=lim_{x->1}[1+(x-1)]^[1/(x-1)]
=e最后答案不是e+1嗎？e^(+1) = elim_{t->0}(1+t)^(1/t) = e,t = x-1.limx趨近于1時(shí)，lim1+(x-1) ^1/x-1=lim1+lim(x-1) ^1/x-1=1+e,難道不是這樣的嗎？？？？x->1, x-1->0啊, (x-1)^[1/(x-1)] 不趨于e. 只有當(dāng)?shù)宗呌?,指數(shù)趨于無(wú)窮時(shí),整個(gè)極限才可能趨于e. lim_{n->無(wú)窮}(1+1/n)^n = e.lim_{t->0}(1+t)^(1/t) = e.lim_{x->無(wú)窮}(1+1/x)^x = e.