3. Determine the Fourier series expansion of the following periodic function: f(t) = { 1 + t₁ 1, t, A. B. C. D. || || || 9 4 + 9 5 + 9-4 + 5 5 y=4+ 9 5 + 00 n=1 00 n=1 ∞ ΣΗ n=1 [сos nπ - 1 η2π n=1 [сos nπ - 1 nn сos n n² [сos nπ n COS -5

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 75E
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3. Determine the Fourier series expansion of the following periodic function:
1,
f(t) = { ₁ + 1
t,
A.
B.
C.
D.
y =
9 5
9
9
y = =+-
4
y = 4
+
914
5
T
5
+-
Σ
5-
5
y ==+=
∞
TU
n=1
n=1
M8
n=1
∞
∞
n=1
[сos nπ
n²π
[сos nπ - 1
nπT
1
[cos nπ
n
-5<t<0
0<t<5
COS
COS
COS
nat
5
nπt
5
nπt
5
сos nπ- 1 nπt
COS +
n²
5
+
COS Nπ
n
-sin
COS NÃ
n²
-sin
COS NTT
TT
сos nπ- 1
n²π
nπt
5
sin
nπt
5
sin
nπt]
5
nπt]
5
Transcribed Image Text:3. Determine the Fourier series expansion of the following periodic function: 1, f(t) = { ₁ + 1 t, A. B. C. D. y = 9 5 9 9 y = =+- 4 y = 4 + 914 5 T 5 +- Σ 5- 5 y ==+= ∞ TU n=1 n=1 M8 n=1 ∞ ∞ n=1 [сos nπ n²π [сos nπ - 1 nπT 1 [cos nπ n -5<t<0 0<t<5 COS COS COS nat 5 nπt 5 nπt 5 сos nπ- 1 nπt COS + n² 5 + COS Nπ n -sin COS NÃ n² -sin COS NTT TT сos nπ- 1 n²π nπt 5 sin nπt 5 sin nπt] 5 nπt] 5
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