A function f(x) = 2 -x2 is defined in the domain [0,1 ]. Show how it can be cont

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A function f(x) = 2 -x2 is defined in the domain [0,1 ]. Show how it can be continued to give a periodic function (that is, make a hand-drawn graph of 3 or 4 periods) such that each of the following conditions (a,b,c,d) is true. Note: Your answers for some parts of a,b,c,d may be the same as for other parts. Also, do not evaluate any of these series; words and graphs are sufficient. Its Fourier series has only cosine terms (except possibly for a constant). Its Fourier series has only sine terms (except possibly for a constant). Its Fourier series has period 1. Its Fourier series has period 2. Would there be any difference between the values of the series in cases c) and d) at x = 0? What about at x = 1? Explain.

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