Real Analysis 45 | Taylor's Theorem

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Пікірлер: 25

@lucaug10 3 жыл бұрын

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! :)

@thomasjefferson6225 Жыл бұрын

Gotta say this whole video series is an amazing public service

@fastundercoverkitgoogle7381 3 жыл бұрын

Damn. Writing (x - x_0) as h makes the formula so much easier to remember! Great work as always

@brightsideofmaths 3 жыл бұрын

Thank you :)

@jamespashley8646 9 ай бұрын

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

@brightsideofmaths 9 ай бұрын

Maybe the next video can help you!

@jamestanny849 9 ай бұрын

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 9 ай бұрын

It's the equation of the tangent + error term :)

@jamestanny849 9 ай бұрын

@@brightsideofmathsyea, after looking more into it it made perfectly sense!

@JojiThomas7431 3 жыл бұрын

Good video. Thanks

@jan861 3 жыл бұрын

Why do we need h^2 for the quadratic approximation ?

@brightsideofmaths 3 жыл бұрын

The h^2 makes it a quadratic approximation :)

@jan861 3 жыл бұрын

@@brightsideofmaths But why exactly ? :D

@brightsideofmaths 3 жыл бұрын

@@jan861 Quadratic approximation means approximation with a polynomial of degree 2, which means h has the power 2 :)

@jan861 3 жыл бұрын

@@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...?

@brightsideofmaths 3 жыл бұрын

@@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.