What makes the natural log “natural”? | Lockdown math ep. 7

From 3Blue1Brown.

All about ln(x).
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Beautiful pictorial summary by @ThuyNganVu:
https://twitter.com/ThuyNganVu/status/1259288683489849344

Errors:
At 16:00, the sum should be written with a "…" to indicate going to infinity.
At 38:41, the exponent should have 1/(2s^2) instead of 1/s^2 for s to represent standard deviation.
At 54:33, an equal sign was mistakenly used in taking the derivative of x^3 / 3!.
At the end, it should be pointed out that the alternating series with x^n terms only converges for values of x between -1 and 1, so the values one can’t be considered proven with values of x outside that range. Everything with the argument here is fine, as it only deals with the convergent input, but that fact should still be mentioned.

Related videos.
Calculus series:
https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

The sum giving pi^2 / 6:
https://youtu.be/d-o3eB9sfls

The sum giving pi / 4:
https://youtu.be/NaL_Cb42WyY
https://youtu.be/00w8gu2aL-w (Mathologer)

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