Please show a step-by-step solution. Do not skip steps, and explain your steps. Write it on paper, preferably. Make sure the work is clear. 6. (a) Calculate the Fourier Series of f(x) = |x|, -^ < x < ^.(b) Draw the 27-periodic function which the series converges to, over the interval-3π < x < 3π.(c) Does the series converge absolutely or conditionally? Does it converge uniformly?Why or why not?(d) Use your result to calculatek=11(2k-1)²andk=11(2k-1)4*

According to the Bartleby guidelines, I will answer first three subparts of a multiple subpart…

6. (a) Calculate the Fourier Series of f(x) = |x], −1 < x < T. (b) Draw the 2-periodic function which the series converges to, over the interval -3π < x < 3π. (c) Does the series converge absolutely or conditionally? Does it converge uniformly? Why or why not? (d) Use your result to calculate k=1 1 (2k-1)² and k=1 1 (2k-1)4*

6. (a) Calculate the Fourier Series of f(x) = |x], −1 < x < T. (b) Draw the 2-periodic function which the series converges to, over the interval -3π < x < 3π. (c) Does the series converge absolutely or conditionally? Does it converge uniformly? Why or why not? (d) Use your result to calculate k=1 1 (2k-1)² and k=1 1 (2k-1)4*

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Please show a step-by-step solution. Do not skip steps, and explain your steps. Write it on paper, preferably. Make sure the work is clear.

6. (a) Calculate the Fourier Series of f(x) = |x|, -^ < x < ^.
(b) Draw the 27-periodic function which the series converges to, over the interval
-3π < x < 3π.
(c) Does the series converge absolutely or conditionally? Does it converge uniformly?
Why or why not?
(d) Use your result to calculate
k=1
1
(2k-1)²
and
k=1
1
(2k-1)4*

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