Fourier Series (a) Sketch the function e for the entire domain of x. (b) Considering the function e¯x in the domain −1 ≤ x ≤ 1, sketch its Fourier series representation (show at least three periods). (c) Without detailed calculation, explain whether the above Fourier series would contain only sine terms, only cosine terms, or both. (d) Considering the function e-x in the domain 0 ≤ x ≤ 1, sketch its Fourier sine series representation (show at least three periods). (e) Considering the function e¯x in the domain 0 ≤ x ≤ 1, sketch its Fourier cosine series representation (show at least three periods).

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