lim[(x-1)/(x+1)]^(x+2) X趋近于无穷大,求极限
问题描述：
lim[(x-1)/(x+1)]^(x+2) X趋近于无穷大,求极限
答
[(x-1)/(x+1)]^(x+2) = [1 - 2/(x+1)]^(x+2)
let t=(x+1)/2
[(x-1)/(x+1)]^(x+2) = [1 - 1/t]^(2t+1) = [(1 - 1/t)^t]^2 * (1 - 1/t)
lim (1 - 1/t)^t = 1/e
lim (1 - 1/t) = 1
lim [(x-1)/(x+1)]^(x+2) = 1/e²