Solved: Let g be the function g(t) = 3 + 4 sin t 5 4 cost for 0 t 2. Use a computer to

Chapter 10, Problem T1

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Let g be the function g(t) = 3 + 4 sin t 5 4 cost for 0 t 2. Use a computer to determine the Fourier coeffi- cients ak bk 3 = 1 2 0 3 + 4 sin t 5 4 cost ! cos kt sin kt3 dt for k = 0, 1, 2, 3, 4, 5. From your results, make a conjecture about the general expressions for ak and bk . Test your conjecture by calculating 1 2 a0 +- k=1 (ak cos kt + bk sin kt) on the computer and see whether it converges to g(t).

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