So I have been using the following link to try to understand the Maclaurin Series: Link. I was given an explanation in class, but it didn't explain things enough, so I have tried Khan Academy.
I understand that a Maclaurin series is approximating another function using a polynomial. However, I don't understand the form that is used in both the Khan Academy video, and the explanation my teacher gave me:
So the definition with the a terms is what I learned from my math class, and the one with the f(0) terms is from the Khan academy video.
So focusing on the second one, I have a few questions:
Why do the factors and x powers correspond to integrating? For instance, if you look at the third term with x^2 and 1/2, then look at the second term, which multiples by 1/3, it seems like the process of integrating (or anti differentiating, whichever you prefer). Why is that?
Also, is there some intuitive explanation for why we use derivatives in the first place? Why does that, of all things, help us approximate or mimic a function?
I appreciate any help, as I am still grappling with this topic.
Thanks!
Best Answer
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