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(4) In order to determine the sum : Fourier series of f found in part 3 is the value of r that needs to be substituted in the a. 1 b. a e. 0 d. None af the above. (5) The sum is a. 45 b. 90 C. 96 d. None af the above.

(4) In order to determine the sum : Fourier series of f found in part 3 is the value of r that needs to be substituted in the a. 1 b. a e. 0 d. None af the above. (5) The sum is a. 45 b. 90 C. 96 d. None af the above.

Advanced Engineering Mathematics
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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fourier series part 4 5
Consider the 27-periodic function defined on [-x, "] by: S(x) = n² – x² (1) The function f is a. even because f(-x) = f(x), Vx E [-x,7] b. odd because f(-2) - -f(x), Vz € [-x, «] c. odd because its graph has a symmetry with respect to the origin d. None of the above. (2) Based on the parity of the function found in part 1, the fourier series S;(r) of f(x) is of the form: +00 a. Sp(x) = tn sin(nr) too b. Sf(2) = ao +4.cos(nx) c. Sf(x) = ao +Ean cos(nar) n=1 d. None of the above (3) The Fourier series of f is then given by: 27 (-1)" cos(7næ) a. S;(2) = Σ 3 n=1 (-1)" cos(n.72) +00 b. S;(r) = 3 +00 (-1)" sin(nr) c. Sy(2) = 2) d. None of the above (4) In order to determine the sum the value of r that needs to be substituted in the Fourier series of f found in part 3 is а. 1 b. I c. 0 d. None af the above. (5) The sum is a. 45 b. 90 C. 96 d. None af the above.
Transcribed Image Text:Consider the 27-periodic function defined on [-x, "] by: S(x) = n² – x² (1) The function f is a. even because f(-x) = f(x), Vx E [-x,7] b. odd because f(-2) - -f(x), Vz € [-x, «] c. odd because its graph has a symmetry with respect to the origin d. None of the above. (2) Based on the parity of the function found in part 1, the fourier series S;(r) of f(x) is of the form: +00 a. Sp(x) = tn sin(nr) too b. Sf(2) = ao +4.cos(nx) c. Sf(x) = ao +Ean cos(nar) n=1 d. None of the above (3) The Fourier series of f is then given by: 27 (-1)" cos(7næ) a. S;(2) = Σ 3 n=1 (-1)" cos(n.72) +00 b. S;(r) = 3 +00 (-1)" sin(nr) c. Sy(2) = 2) d. None of the above (4) In order to determine the sum the value of r that needs to be substituted in the Fourier series of f found in part 3 is а. 1 b. I c. 0 d. None af the above. (5) The sum is a. 45 b. 90 C. 96 d. None af the above.
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