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t = -1,t = 0,t =1,... 3. Verify the result shown using 'integration by parts'. 1 1 |t sin(nt) dt = -; t cos(nt) + sin(nt) n n2

t = -1,t = 0,t =1,... 3. Verify the result shown using 'integration by parts'. 1 1 |t sin(nt) dt = -; t cos(nt) + sin(nt) n n2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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Let f(x) be a function of variable x defined on an interval 0 to T. It can be represented by the Fourier series, given by {(2) = +Ean 2nn (2nt +> an cos T *) + b, sin T where 2nt 2na f(u)du, an ( r(u) cos (u) du, b. -и) du, bn T I f(u) sin ao = -u) du. Answer the following questions. 2. Explain the meaning of Gibbs phenomenon, using the function ƒ defined above as an example. Show how the errors behave as t gets closer to one of the points t = -1,t= 0, t = 1, .. 3. Verify the result shown using 'integration by parts'. 1 1 | t sin(nt) dt = -- t cos(nt) + sin(nt) n2 n
Transcribed Image Text:Let f(x) be a function of variable x defined on an interval 0 to T. It can be represented by the Fourier series, given by {(2) = +Ean 2nn (2nt +> an cos T *) + b, sin T where 2nt 2na f(u)du, an ( r(u) cos (u) du, b. -и) du, bn T I f(u) sin ao = -u) du. Answer the following questions. 2. Explain the meaning of Gibbs phenomenon, using the function ƒ defined above as an example. Show how the errors behave as t gets closer to one of the points t = -1,t= 0, t = 1, .. 3. Verify the result shown using 'integration by parts'. 1 1 | t sin(nt) dt = -- t cos(nt) + sin(nt) n2 n
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