Consider the function defined by f(x) =1-x, 0...
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Consider the function defined by f(x) =1-x, 0<x<1, (a) Sketch the even periodic extension for the function f. [3 marks] (b) Determine the Fourier sine (odd) series representation for the function f. [6 marks] (c) Determine the Fourier cosine (even) series representation for the function f. [8 marks] 1 =1+ + 3 5 7? 1 1 (d) Evaluate the cosine series at x-0. Hence show that 8 [3 marks] .... Consider the function defined by f(x) =1-x, 0<x<1, (a) Sketch the even periodic extension for the function f. [3 marks] (b) Determine the Fourier sine (odd) series representation for the function f. [6 marks] (c) Determine the Fourier cosine (even) series representation for the function f. [8 marks] 1 =1+ + 3 5 7? 1 1 (d) Evaluate the cosine series at x-0. Hence show that 8 [3 marks] ....
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