Question

Why does lim (1 + 1/x)^x when x tends to + inf, equals e?

Answer 1

You know \[e ^{\ln x}\] is always equal to x. Just try doig the same thing there and you'll see what will happen.

Answer 2

I really don't get it, would you mind to explain a bit more?

Should I do: \[\lim_{x \rightarrow \infty} e^{\ln (1+1/x)^x} \]

Answer 3

Perhaps by definition. Let that limit equal a value we call e.

Answer 4

you would still need to prove that the limit converges.