5. Determine the half-range sine series expansion of the following: f(t) = t² + t, A. B. C. D. y = 4 = 4 Σ[(C05 y = 4 ΣΙ n=1 y n=1 y = 4 4Σ ( n=1 сos nπ nπ сOS nπ (nπ)³ сos nπ (nπ)² + = 4 Σ[(-²-² n=1 сos nπ nπ соs nл + 1 (nn)³ + 0 < t < 1 + COS Nπ nπ соs nл + 1 (nπ)³ COS Nπ- (nπ)³ 1 1 sin nët nnt] sin nat sin not sin nat
5. Determine the half-range sine series expansion of the following: f(t) = t² + t, A. B. C. D. y = 4 = 4 Σ[(C05 y = 4 ΣΙ n=1 y n=1 y = 4 4Σ ( n=1 сos nπ nπ сOS nπ (nπ)³ сos nπ (nπ)² + = 4 Σ[(-²-² n=1 сos nπ nπ соs nл + 1 (nn)³ + 0 < t < 1 + COS Nπ nπ соs nл + 1 (nπ)³ COS Nπ- (nπ)³ 1 1 sin nët nnt] sin nat sin not sin nat
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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Transcribed Image Text:5. Determine the half-range sine series expansion of the following:
f(t) = t2 + t,
Α.
Β.
C.
D.
y = 4
y = 4
ΑΣΙ
η=1
00
ΣΙ
η=1
y = 4
ΑΣΚ
η=1
y = 4
∞
ΣΙ
η=1
COS Nπ
ηπ
COS Nπ
(ηπ)3
сos nπ
(ηπ)2
+
сOS Nπ
ηπ
cos nπ + 1
(ηπ)3
+
0 <t < 1
+
cos ηπ – 1
ηπ
cos ηπ + 1)
(ηπ)3
COS Nπ
(ηπ)3
1
sin nat
sin nat
sin nat
sin not
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