Deriving e from the limit (1+1/x)^x as x approaches infinity

[Ursus-tllt]

You cant use ln in your proof since ln is based on e and its derivative is based on the results of this theorem.
The actual proof is complicated and it just proves the limit exists and is between 2 and 3, than it is calculated with taylor approximation

[isabellamichalek]

hello, thank you for your video, but I am confused about how you canceled the -1/x^2.

[prakashlakhapate]

You can not use natural logarithm as E is to be proved. Dhanyavad

[jamesharmon]

What I'd be interested in knowing is what happens if 1/x is replaced by 2/x, or 3/x. Since the given formula converges and one factor is being multiplied by a constant, the new formula should also converge.

[DamienBlt]

I understood all, but at the beguining, why there is (let y) what meaning ?, and what ln y =

[РусскийПатриотЯша]

Idk, there was a n easier method imo, where by using log properties and mclaurin you not only simplify the process but also save up time.

[AbhilashKhuntia]

I am getting stuck like why are we cancelling -1/x^2 won't those two be equal to 0 and we cannot cancel 0 terms like that
Please correct me if I am wrong

[wyboo]

but isn't this limit the definition of e? or are you using the infinite polynomial definition of e^x

[willyprophete]

What will happen if base is 10? ( Then we have log 10 = 1 )

[prakashlakhapate]

Binomial expansion formula need to be used because e is to be proved.

[sweetworldismine]

I just discovered your channel. You are doing a wonderful job. Do you have a Whatsapp or telegram group for Jss1 student's mathematics

[adwz]

ln == log base e, and e is defined by this limit, so nothing was achieved other than showing consistency - there is no need to prove anything, as the definition of e itself is the limit

[willyprophete]

logy = 1 and then y = 10 or lim xlog(1+1/x) = 10 when x is very bigger