n In the interval (−л, π), ³₂ (x) : = √ : exp(-n²x²). (a) Expand &n (x) as a Fourier cosine series. (b) Show that your Fourier series agrees with a Fourier expansion of 8 (x) in the limit as n → ∞. (c) Confirm the delta function nature of your Fourier series by showing that for any f(x) that is finite in the interval [—ë, ë] and continuous at x = 0, T ** f (x) [Fourier expansion of 8% (x)] dx = ƒ(0). -T

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