Question

求解高等数学极限，最好有步骤。

Answer 1

1.     lim<x→1->(x+1)e^[1/(x-1)] = 2 lim<x→1->e^[1/(x-1)] = 0

       lim<x→1+>(x+1)e^[1/(x-1)] = 2 lim<x→1+>e^[1/(x-1)] = +∞ 

       故本题极限不存在。

2.    lim<x→1-> [(x^2-1)/(x-1)] e^[1/(x-1)]

     =  lim<x→1-> (x+1)e^[1/(x-1)] = 0

     lim<x→1+> [(x^2-1)/(x-1)] e^[1/(x-1)]
   

     =  lim<x→1+> (x+1)e^[1/(x-1)] = +∞

     故本题极限不存在。