Very interesting. It seems like we used e to show the very definition of e. Out of curiosity, is there another method to prove this without relying on taking the natural logarithm?
Not that I know of at this point, the exponent n (variable) is not easy to deal with, taking the natural log will bring it down to the front which helps a lot.
It is just like the other properties of a limit such as constant multiplied by a function, where k is the constant, lim[k•f(x)] = k•lim f(x). You can also do it with logarithms. (Please correct me if I am wrong, I self teach myself and I am new to this topic.)
This is a limit for n approaches infinity which only applies where the n term is; you can have ln either inside the limit or outside the limit because they are the same.
I am not complaining , I am just trying to search how this number 've been invented I know the 1+1/n problem but how e and ln was defined in this time I wish see the historical pattern somewhere but I couldn't find it . btw your video was awesome
This is not thanks time why we use differencition in this even derivative is derive from this equation this is common sence questions do it by your mind
أظن أنّ هناك من يعرّف العدد e بهذه الطريقة: lim_(x->∞) [(1+(1/n))^n] ومن ثم يستنتجون بقية الخواص لاحقاً، بمعنى آخر، لا تعتبر هذه الخاصية مما يجب برهانه وإنما هي الأساس الذي يتم استنتاج الأشكال الأخرى للعدد e من خلاله
The point of proving lim_(n->∞) (1+1/n)^n = e is that you need to prove that the limit exists, but not divergent to infinity or something. After all that work, you can safely define e as the limit. Of course this video did none of that.
Man thank you so much, even though im not studying any math course rn, yet this video was so easy to follow.
No problem!
Awesome, keep up the great work!
Thank you!
easily understandable
c'est faux puisque démontre le dérivée de ln (x)v=1/x on a besoin de cette limitr
Thanks, this helps a lot.
Thank you
Thank you, mate,
Very interesting. It seems like we used e to show the very definition of e. Out of curiosity, is there another method to prove this without relying on taking the natural logarithm?
Not that I know of at this point, the exponent n (variable) is not easy to deal with, taking the natural log will bring it down to the front which helps a lot.
@Mathisyourfriend ok thank you!
how can you put the ln inside the limit?
It is just like the other properties of a limit such as constant multiplied by a function, where k is the constant, lim[k•f(x)] = k•lim f(x). You can also do it with logarithms.
(Please correct me if I am wrong, I self teach myself and I am new to this topic.)
@@Hewooo39 yes its true a limit of a function is the limit of the function as long as the limit is a finite number
thanks😊very clear❤
good solution bro
thanks a lot
does this equation have a name? pls answer.....
Hello, I am not sure if there is a specific name for this limit.
how can the ln be put inside the limits? pls answer
This is a limit for n approaches infinity which only applies where the n term is; you can have ln either inside the limit or outside the limit because they are the same.
Cronin Camp
good but you just verified that's it's it equal to this lim you didn't proove it from the beggining
I believe this is ok because I am proving the left side equals the right side. (1+1/n)^n is given.
I am not complaining , I am just trying to search how this number 've been invented I know the 1+1/n problem but how e and ln was defined in this time I wish see the historical pattern somewhere but I couldn't find it . btw your video was awesome
@@francaishaitam6708 No problem! And thank you!
This is not thanks time why we use differencition in this even derivative is derive from this equation this is common sence questions do it by your mind
What is lim (2 + 1/n )^n = ?
Hi, I think the answer is infinity. If you put infinity into n, it is like (2 + 0)^infinity. This is a very very large number.
أظن أنّ هناك من يعرّف العدد e بهذه الطريقة:
lim_(x->∞) [(1+(1/n))^n]
ومن ثم يستنتجون بقية الخواص لاحقاً، بمعنى آخر، لا تعتبر هذه الخاصية مما يجب برهانه وإنما هي الأساس الذي يتم استنتاج الأشكال الأخرى للعدد e من خلاله
The point of proving lim_(n->∞) (1+1/n)^n = e is that you need to prove that the limit exists, but not divergent to infinity or something. After all that work, you can safely define e as the limit. Of course this video did none of that.