why is it that ln(1+u)^(1/u)=1
why is it that as the limit of u approaches zero of ln(u+1)^(1/u)=1? I am trying to figure this out because I want to see the proof of the derivative of lnx = 1/x. I know that ln(u+1)^(1/u)=1 and when I plug in digits in my calculator I see it to be true, however, I cannot see it algebraically why it is true. I cannot see it because I see ln(1)^1/0. To me this is not possible.
Re: why is it that ln(1+u)^(1/u)=1
(letting u = 1/n)
1. we can take the limit inside the ln function, since ln is continuous
2. the number e is often DEFINED as: