e^[1/(x-1)]-1为无穷小，等价于1/(x-1)，——》原式= limx→∞ x/(x-1)=1。
limx*{e^[1/(x-1)]-1} = lim{e^[1/(x-1)]-1}/(1/x) (0/0)= lim [-1/(x-1)^2]e^[1/(x-1)]/(-1/x^2)= lim [x^2/(x-1)^2]e^[1/(x-1)] = lim [x^2/(x-1)^2] * lim e^[1/(x-1)] = 1*1 = 1
