Prove

Question

limit as x approaches +infinity of
(1 + 1/x)^x = e

Answer 1

log f(x) = x log (1 + 1/x)
= x [(1/x) + (1/x)^2 + ...]
= 1 + 1/x + (1/x)^2
I used a well known Taylor series for log (1+x)

Lim log f(x) as x-> infinity = 1
Therefore the limiti of f(x) is e