有问题追问，两小时内在线。
lim(x+1)e^[1/(x-1)] = 2 lime^[1/(x-1)] = 0
lim(x+1)e^[1/(x-1)] = 2 lime^[1/(x-1)] = +∞
故本题极限不存在。
lim [(x^2-1)/(x-1)] e^[1/(x-1)]
= lim (x+1)e^[1/(x-1)] = 0
= lim (x+1)e^[1/(x-1)] = +∞
C. 当x->0时， ln(1+2x)的等价无穷小是2x, 0.5 ln(1+2x)的等价无穷小是x, 而sinx~x,由等价无穷小的传递性，0.5 ln(1+2x)~sinx .故选 C
