(a) Compute the Fourier sine series expansion of f(x) = 3x - x² on [0, 3] (b) To what value does this series converge at x = 1? Explain.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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1. (a) Compute the Fourier sine series expansion of f(x) = 3x – x² on [0, 3].
(b) To what value does this series converge at x = 1? Explain.
2. Solve the initial-boundary value problem
ди
3 a?u
0 <x < 4n, t 0
ди
(0, t)
10 Əx?
ди
. (Απ, t) 0
t > 0
=
0,
0 < x < T
u(x, 0) = {
8,
0 < x < 4n
T < x < 4n
Transcribed Image Text:1. (a) Compute the Fourier sine series expansion of f(x) = 3x – x² on [0, 3]. (b) To what value does this series converge at x = 1? Explain. 2. Solve the initial-boundary value problem ди 3 a?u 0 <x < 4n, t 0 ди (0, t) 10 Əx? ди . (Απ, t) 0 t > 0 = 0, 0 < x < T u(x, 0) = { 8, 0 < x < 4n T < x < 4n
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