原式=lim(x→∞)[1+1/(x+1)]^x
=lim(x→∞)[1+1/(x+1)]^(x+1-1)
=lim(x→∞)[1+1/(x+1)]^(x+1)÷lim(x→∞)[1+1/(x+1)]
=e÷1
=e
【附注】根据两个重要极限，
lim(x→∞)[1+1/(x+1)]^(x+1)=e
(x+2)/(x+1)
=1 + 1/(x+1)
let
1/y = 1/(x+1)
lim(x->∞) [(x+2)/(x+1)]^x
=lim(x->∞) [1 + 1/(x+1)]^x
=lim(y->∞) [1 + 1/y]^(y-1)
=lim(y->∞) [1 + 1/y]^y
=e
内容全部来源于网络收集，如有侵权，请联系网站删除：QQ：24596024