Problem

Find at least three nonzero terms (including $a_{…

Problem 7 Easy Difficulty

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.
$$f(x)=\left\{\begin{array}{rr}
0 & -\pi \leq x<0 \\
x & 0 \leq x<\pi
\end{array}\right.$$

Answer

$f(x)=\frac{\pi}{4}-\frac{2}{\pi}\left(\cos x+\frac{1}{9} \cos 3 x+\cdots\right)$
$+\left(\sin x-\frac{1}{2} \sin 2 x+\cdots\right)$

Related Courses

Calculus 2 / BC

Basic Technical Mathematics with Calculus

Chapter 30

Expansion of Functions in Series

Section 6

Introduction to Fourier Series

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Watch More Solved Questions in Chapter 30

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Video Transcript

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

Get More Help with this Textbook

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

View More Answers From This Book

Find Another Textbook

Problem