Course Solutions Uncategorized (Solved) : 4 Let F X 4 X 0 Q33114244 . . . .

(Solved) : 4 Let F X 4 X 0 Q33114244 . . . .

 

4. Let f(x)-4-x, 0<xS2 (a) Expand f(x) into a periodic function of period 2, ie, construct the function F(x), such that F(x)-f (s), 0 <x 2, and F(x) = F(x + 2) for all real numbers x. (This process is called the full-range expansion of f(x) into a Fourier series.) Find the Fourier series of Fx). Then sketch 3 periods of Fix). Compare the result of this with the two half-range expansions below. Is the Fourier series, Fx), you found an even or an odd function? (b) Sketch 3 periods of the even periodic extension (period 4) of f(x). Find the cosine series. (c) Sketch 3 periods of the odd periodic extension (period 4) of f(x). (d) For each Fourier series, determine the value to which the series converges to at x = 8.4.

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