Question

lim(x趋于无穷)[x/(1+x)]^x

Answer 1

如图

Answer 2

x/(1+x)= 1 - 1/(1+x)
let
1/y = 1/(1+x)
lim(x->∞)[x/(1+x)]^x
=lim(x->∞)[1 - 1/(1+x)]^x
=lim(y->∞)(1 - 1/y)^(y-1)
=lim(y->∞)(1 - 1/y)^y
=e^(-1)