Let f(x) be a periodic function of period 27 defined by f(r) = x - x2 in (-7, 7). (i) Draw the graph of f(r) in [-3T,37]. (the coordinate of points at which the curve intersects the coordinate axes should be clearly written in the graph). (i) Find f (). (iii) Find the Fourier series of f(x). (iv) Using the Fourier series you obtained, check whether the series 1 1 12 22 32 42 converges. If it converges, to what values it converge?
Let f(x) be a periodic function of period 27 defined by f(r) = x - x2 in (-7, 7). (i) Draw the graph of f(r) in [-3T,37]. (the coordinate of points at which the curve intersects the coordinate axes should be clearly written in the graph). (i) Find f (). (iii) Find the Fourier series of f(x). (iv) Using the Fourier series you obtained, check whether the series 1 1 12 22 32 42 converges. If it converges, to what values it converge?
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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