1. Consider the function f defined by f (x) =| sin x |, for - T < x < T. a) Find the Fourier series of f. b) Sketch the graph of the function to which the series converges point- wise on R. Use the pointwise convergence theorem to justify your answer. c) By choosing a suitable value of x in the series that you have found, show that Ek=14k2 – 1 1 || 2° |

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. Consider the function f defined by
f (x) =| sin x |, for
- T < x < T.
a) Find the Fourier series of f.
b) Sketch the graph of the function to which the series converges point-
wise on R. Use the pointwise convergence theorem to justify your
answer.
c) By choosing a suitable value of x in the series that you have found,
show that Lk=14k2 – 1
1
2
Transcribed Image Text:1. Consider the function f defined by f (x) =| sin x |, for - T < x < T. a) Find the Fourier series of f. b) Sketch the graph of the function to which the series converges point- wise on R. Use the pointwise convergence theorem to justify your answer. c) By choosing a suitable value of x in the series that you have found, show that Lk=14k2 – 1 1 2
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