I need a proof that lim(1+1/x)^x=e.

We defined that e=lim(1+1/n)^n and I need to prove that it's same for x (real number).

Thanks.

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- Apr 21st 2013, 06:06 AMkicmalim (1+1/x)^x
I need a proof that lim(1+1/x)^x=e.

We defined that e=lim(1+1/n)^n and I need to prove that it's same for x (real number).

Thanks. - Apr 21st 2013, 06:39 AMBradynsRe: lim (1+1/x)^x
The question seems trivial, as:

Is the exact same statement as:

Just let n = x.

Though, this also seems trivial.. Even if they were integers or natural numbers, it would still approach the value of 'e' as the limit went to infinity.

Have you done the proof for the 'n' in class? - Apr 21st 2013, 07:14 AMPlatoRe: lim (1+1/x)^x
- Apr 21st 2013, 08:07 AMx3bnmRe: lim (1+1/x)^x
We know that:

and as so

Using I'Hopital's rule:

- Apr 21st 2013, 08:20 AMPlatoRe: lim (1+1/x)^x
- Apr 21st 2013, 08:23 AMx3bnmRe: lim (1+1/x)^x