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Find at least three nonzero terms (including $a_{0}$ and at least two cosine terms and two sine terms if they are not all zero) of the Fourier series for the given functions, and sketch at least three periods of the function.$$f(x)=\left\{\begin{array}{rr}0 & -\pi \leq x<0 \\x^{2} & 0 \leq x<\pi\end{array}\right.$$

Calculus 2 / BC

Chapter 30

Expansion of Functions in Series

Section 6

Introduction to Fourier Series

Series

Oregon State University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

02:05

In the following exercises…

03:34

Find the first three nonze…

08:33

Find the Fourier series of…

06:33

03:37

01:15

Use the even/odd propertie…

02:39

01:56

09:44

we want to find the 1st 3 turns of the MacLaurin series for Natural Log of Co signed X. Well, if we take the derivative well, let's call this f of X. We take the derivative of F of X. We get one over co sign X times, the derivative coast on its, which is minus sign X, and we get minus tangent tax. Now we know that the MacLaurin series for a tangent x is X plus 1/3 X cubed plus 2 15 x to the fifth and we're only talking wheeling in the 1st 3 terms from We're going to stop there. So the MacLaurin series for minus Tanja necks is just the negative of that minus X minus 1/3 X cubed minus 2 15 Sex to the fifth minus. And now, to find MacLaurin series for F of X, we just integrate turned by term. So yet minus X squared over too minus X to the fourth times for thirds. I'm sorry. Mine, Uh, times they're over 12 right? And then minus. It's gonna be a next to the sixth one divided by six. So too, over 90. And so on

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