.. Consider the 1-periodic Fourier series expansion ao 9+2 {an cos(2 nnx) + bn sin(2 nmx)} of the function f(x) = ‹ 2 n=1 To which value does it converge at x = 5/2? (A) 0 (B) 1 (C) 1/2 (D) 3 Solution. Since S(r) is 1-periodic, S(5/2) = S(1/2) = [4x², 0
.. Consider the 1-periodic Fourier series expansion ao 9+2 {an cos(2 nnx) + bn sin(2 nmx)} of the function f(x) = ‹ 2 n=1 To which value does it converge at x = 5/2? (A) 0 (B) 1 (C) 1/2 (D) 3 Solution. Since S(r) is 1-periodic, S(5/2) = S(1/2) = [4x², 0
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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Please explain the highlighted part. Why is because it's 1-periodic, S(1/2) is equal to S(5/2). Please explain how the question would change if it were 2-periodic instead. Thx
Transcribed Image Text:3.
Consider the 1-periodic Fourier series expansion
+도
+ {an cos(2nㅠr) + bn sin(2nx)} of the function f(x) =
2
n=1
To which value does it converge at x = 5/2?
(A) 0
(B) 1
(C)
1/2
Solution. Since S(r) is 1-periodic,
S(5/2) = S(1/2)
[4x2, 0≤x< 호
11/x, 흐드æ<1.
f(1/2+) + f(1/2-) 2+1
2
2
(D)3
→ (E) 3/2
+
f(xt) + f(x)=f(ttf(호)
=
2
2
=
2+1 = 3
쓸
2
3-2
2
1
t
초
Q
2
24(월)2
-IN
+
2
1
= 1 0드리드를
2
호드 XC1
2
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