Question 12. Consider the function ø(x) = e + x. 2 12a. W down the Fourier series and the Fourier cosine series of ø(x) on the interval x E (0, 1) but leave your coefficients as integrals. 12b. Write down the full Fourier series of ø(x) on the interval x E (-1,1) but leave your coefficients as integrals. 12c. At the point x = 0, what number does the Fourier sine series in 8a converge to? In other words, if we take more and more terms in the sum and evaluate at x = 0, what number will we get close to? What number does the Fourier cosine series in 12a converge to? What number does the full Fourier series in 12b converge to? 12d. For each series, plot the function that the Fourier series will get closer to (converge to) on the interval x E (-2, 2).

Question 12. Consider the function ø(x) = e + x. 2 12a. W down the Fourier series and the Fourier cosine series of ø(x) on the interval x E (0, 1) but leave your coefficients as integrals. 12b. Write down the full Fourier series of ø(x) on the interval x E (-1,1) but leave your coefficients as integrals. 12c. At the point x = 0, what number does the Fourier sine series in 8a converge to? In other words, if we take more and more terms in the sum and evaluate at x = 0, what number will we get close to? What number does the Fourier cosine series in 12a converge to? What number does the full Fourier series in 12b converge to? 12d. For each series, plot the function that the Fourier series will get closer to (converge to) on the interval x E (-2, 2).

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

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