lim((x+2)/(x-3))^(x-1)

看你初学，给你说详细点。

令x-3=t
则((x+2)/(x-3))^(x-1)
=(1+5/t)^(t+2)
=(1+5/t)^2*(1+5/t)^t

再令5/t=u，上式
=（1+u)^2*[(1+u)^(1/u)]^5,

u趋于0，极限显然为e^5.

lim((x+2)/(x-3))^(x-1)
=lim[(1+5/(x-3))^(x-3)/5]^5(x-1)/(x-3)
=[lim(1+5/(x-3))^(x-3)/5]^lim5(x-1)/(x-3)
=e^5.

^这个是什么意思？