Second last step: you need to use "continuity" of ln(x). (Because:with still finite x/h the term in the ln is not yet 'e'). BTW: I love the way you are presenting this explaining every step (in a calm and friendly way). Most teachers try to do it in a hurry. That is the main reason, why some students get annoyed with math.
If you define ln(x) as the integral from 1 to x of 1/u du, you have no problems computing its derivative. It is equal to 1/x by definition of the function.
Hello sir, i'm seeing that we always using definition of e with limit while proving all of these formulas but is it actually possible for you to explain or prove how or why limit n->infinity (1+1/n)^n is equal to euler's number? Did you record a video about this or would you talk about that in another video if it's possible? Thanks
just a suggestion 😁 It might be too late to point out but, you could have started by first proving that ln(x) is indeed differentiable by Left and Right hand derivative then go on to find it.
This works because lim x-> -inf (1+1/x)^x is also equal to e, but I don't know any proofs without using the derivative of ln(x) (this would be circular reasoning).
Second last step: you need to use "continuity" of ln(x). (Because:with still finite x/h the term in the ln is not yet 'e').
BTW: I love the way you are presenting this explaining every step (in a calm and friendly way). Most teachers try to do it in a hurry. That is the main reason, why some students get annoyed with math.
I never thought of this! Good job!
If you define ln(x) as the integral from 1 to x of 1/u du, you have no problems computing its derivative. It is equal to 1/x by definition of the function.
8:58 as h goes to 0, "n" or x/h goes to infinity. Thus, lim as h goes to 0 = lim n goes to infinity.
Hello sir, i'm seeing that we always using definition of e with limit while proving all of these formulas but is it actually possible for you to explain or prove how or why limit n->infinity (1+1/n)^n is equal to euler's number? Did you record a video about this or would you talk about that in another video if it's possible? Thanks
Beautiful! 1st time seeing this truly from first principles!
This guy turns math into magic
just a suggestion 😁
It might be too late to point out but, you could have started by first proving that ln(x) is indeed differentiable by Left and Right hand derivative then go on to find it.
😍😍👌👌✊✊👍👍
(1 + 1/(x/h))^(x/h) is not equal e
as h approaches 0, x over h approaches infinity, if you replace x/h with a variable it's more legible
the enthusiasm made this really enjoyable to watch, great job
Very good explanation ❤
He missed step when he used fact that ln is continuous
5:31, as h goes to zero wouldn't x/h go to either positive infinity or negative infinity?
This works because lim x-> -inf (1+1/x)^x is also equal to e, but I don't know any proofs without using the derivative of ln(x) (this would be circular reasoning).
Recall that the domain of ln (x) is **positive real numbers only** hence x/h is a positive real number x divided by a quantity h tending to zero
Love your videos
Love this
But n is integer while x/h is real number?
Great job
You are AWESOME!!
I really like your classes, thank you for your hard work! 😃
You are the best
Very good. Thanks 👍
It's very useful to understand the inderivatived integral of dx/x sir!
Use grouping symbols: (dx)/x
You are a great man
BRAVO
You are the best
Thank you for your kind words.
Awesome
Always the best teacher.....what about 1/x
Thanks
Solid videos!