(2) Let ƒ : [-x, 7] → R be defined by 0 if – a

Trigonometry (MindTap Course List)
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ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
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ChapterA: Appendix: Review Topics
SectionA.3: Introduction To Functions
Problem 43PS
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DO (a) to (d)
(2) Let ƒ : [-a , 7] → R be defined by
0 if - T<x <-5,
1 if -<x < 0,
0if 0<x < T.
f(x)
(a)
Calculate the complex Fourier series of f.
Let F : R → R be the function to which the complex Fourier series of f
(b)
converges. Sketch the graph of F on the domain [-27, 2T].
(c)
series of f converges pointwise to F?
What is it about the function ƒ that guarantees that the complex Fourier
(d)
Does the complex Fourier series of f converges uniformly to F? Why or why
not?
Transcribed Image Text:DO (a) to (d) (2) Let ƒ : [-a , 7] → R be defined by 0 if - T<x <-5, 1 if -<x < 0, 0if 0<x < T. f(x) (a) Calculate the complex Fourier series of f. Let F : R → R be the function to which the complex Fourier series of f (b) converges. Sketch the graph of F on the domain [-27, 2T]. (c) series of f converges pointwise to F? What is it about the function ƒ that guarantees that the complex Fourier (d) Does the complex Fourier series of f converges uniformly to F? Why or why not?
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