As a CS major, I used Landau symbols all the time to describe the complexity of algorithms, but never knew the symbol actually had this name! The more you know hahahah Great video as always! :)
I lost track at 2:11, when you introduced the equation for f(x0 + h). Could you please explain exactly how you came up with this equation, why is it this equation and how this relates to the pictured graph. Thank you!
@@brightsideofmaths But I thought this is what the term 1/2 * f''(x0)*h^2 is used for. And r(h) is the rest function, isn't it? I thought we need a separate rest function r2(h) for the quadratic approximation. But somehow the linear rest function also works for the quadratic approximation...?
@@jan861 I didn't give the rest function a new name. This means that the rest function for the quadratic approximation is a different one than the one from the linear approximation, in general.
As a CS major, I used Landau symbols all the time to describe the complexity of algorithms, but never knew the symbol actually had this name! The more you know hahahah
Great video as always! :)
Gotta say this whole video series is an amazing public service
Damn. Writing (x - x_0) as h makes the formula so much easier to remember! Great work as always
Thank you :)
I lost track at 2:11, when you introduced the equation for f(x0 + h). Could you please explain exactly how you came up with this equation, why is it this equation and how this relates to the pictured graph. Thank you!
It's the equation of the tangent + error term :)
@@brightsideofmathsyea, after looking more into it it made perfectly sense!
I'm confused about just one thing; what do you mean by the remainder of h, or r(h)?
what does it represent and how do you work it out
Maybe the next video can help you!
Good video. Thanks
Why do we need h^2 for the quadratic approximation ?
The h^2 makes it a quadratic approximation :)
@@brightsideofmaths But why exactly ? :D
@@jan861 Quadratic approximation means approximation with a polynomial of degree 2, which means h has the power 2 :)
@@brightsideofmaths But I thought this is what the term 1/2 * f''(x0)*h^2 is used for. And r(h) is the rest function, isn't it? I thought we need a separate rest function r2(h) for the quadratic approximation. But somehow the linear rest function also works for the quadratic approximation...?
@@jan861 I didn't give the rest function a new name. This means that the rest function for the quadratic approximation is a different one than the one from the linear approximation, in general.
How to derive that is not the part of video, what a mystery !
What do you mean?
gibts die Videoreihe auch auf deutsch?
Not yet.
Interesting acent😂
It's German :D
Bro sounds like pewdiepie
Okay :D
400th like :3