3blue1brown
@3blue1brown·8.4M subscribers·240 videos
What makes the natural log "natural"? | Ep. 7 Lockdown live math
Posted
May 8, 2020
Views
1,717,061
Likes
26,927
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Engagement
1.65%
May 8, 2020
1,717,061
26,927
1,409
1.65%
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1:14:54Now PlayingAll about ln(x).
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Beautiful pictorial summary by @ThuyNganVu:
Errors:
At minute 16, the sum should be written with a "..." to indicate going to infinity.
At minute 38, the exponent should have 1/(2s^2) instead of 1/s^2 for s to represent standard deviation.
At minute 54, 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:
The sum giving pi^2 / 6:
The sum giving pi / 4:
(Mathologer)
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
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Music by Vincent Rubinetti.
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