Wth

[lone drift]

https://youtu.be/HPcoTR1piAA?si=LDrFcZ9LcuKNbV74 whats this guy on about?

[grave wharf]

wtf it is taylor expansion i think, why is it called that way

$f(x)=\sum_{n=0}^{\infty} \frac {f^{(n)}(a)} {n!} (x-a)^n$

[fiery rivet]

Tangent

[grave wharf]

i think

yes

[fringe obsidian]

It’s a way to approximate any functions in the neighborhood of some point.
For example in that video, the neighborhood is x=b.

Any functions can be approximated with a polynomial. As long as we stay in the « neighborhood » considered

Imagine You got some function f(x). And you have some infos about this function:
f(20)=4
f’(20)=7

Basically you got infos when x=20

And they want you to give an approximation of f(20.3)

20.3 is very close to 20, it’s in the « neighborhood » of 20.

Then you can use series expansion:

f(20.3)=f(20)+f’(20)(20.3-20)

[grave wharf]

yeah it is called a taylor expansion