Construct the Fourier sine series and the Fourier cosine series of the given function f. In each case, discuss the convergence of the series on the interval [0,L] where f is defined, and sketch the functions to which the series converges pointwise on [-3L,3L].

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6 f(x) = 3x+1, 0≤x≤ 2. 6 f(x) = 3x+1, 0≤x≤ 2.