重要极限lim[x+1/(x-1)]^(x-2)最后得出e^2/(x-1)*2到这里我会,最后怎么变e^2啊?x趋向于无穷不好意思，再问下[e^2/(x-1)]*2在什么情况下等于e^2啊

Question

重要极限
lim[x+1/(x-1)]^(x-2)最后得出e^2/(x-1)*2到这里我会,最后怎么变e^2啊?
x趋向于无穷
不好意思，再问下[e^2/(x-1)]*2在什么情况下等于e^2啊

Answer 1

lim[x+1/(x-1)]^(x-2)
= lim[1+(2/(x-1))]^(x-1) / [1+(2/(x-1))]
= lim e^2 / [1]
= e^2
没问题啊...
x趋向于无穷 e^2/(x-1)*2 趋向于0
这个什么问题...
--------------------------
e^2/(x-1) *2=e^2
1/(x-1) *2=1
(x-1) =2
x=3
oh, yes...
x+1/(x-1) x+1要+括号的 不然会发散的...oh...