e graph of the
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Can you answer b
Transcribed Image Text:The function f is defined for 0 < x < 2 by
0 if 0<x< 1,
3 if 1 < x < 2;
Find the coefficients of the Fourier sine series for f(x).
f(x) =
b) Sketch the graph of the function to which the Fourier sine series converges
on -6 ≤ x ≤ 6. Use X's to mark points showing what the Fourier sine series converges
to at jump discontinuity.
Expert Solution
Step 1
Here, in part b we have to sketch the graph of the function to which fourier sine series converges on . We have to use to mark points showing what the Fourier sine series converges to a jump discontinuity. We have to see to it how the converge is taking place.
How can we determine the Fourier series' convergence at a point of discontinuity?
It has been explored how to describe such a function using a Fourier series, and it has been noted that this series converges at the point of discontinuity to the average value between the function's two limits relative to the jump point.
Therefore, this convergence for a step function occurs at the exact value of one half.
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