L'hopital's rule limit?? Find the limit as x approaches infinity...(x/(x+1))^x?

Question

Find the limit as x approaches infinity...

(x/(x+1))^x

how do you do this??

Answer 1

I believe that you know Lim (x --> ∞) (1 + 1/x)^x = e.
Therefore Lim (x --> ∞) (x/(x+1))^x
= Lim (x --> ∞) {[(x+1)/x]^(x)}^(-1)
= Lim (x --> ∞) [(1 + 1/x)^x]^(-1)
= 1/e