## Question

###### Consider the periodic functionsin t for 0 < t<3 f(t) (o for $ < <t f(t+#) =f():(a) Sketch this function over the interval -27 < t < 21 [4] (b) State whether this function is even. odd, neither . [1] (c) Find the Fourier series for this function To obtain full marks. your final answer should be simplified so that it does not contain any terms of the form cos 5 sin $ where kis an integer, [20] (d) By considering pointwise convergence of this Fourier series at t = evaluate the sum

Consider the periodic function sin t for 0 < t<3 f(t) (o for $ < <t f(t+#) =f(): (a) Sketch this function over the interval -27 < t < 21 [4] (b) State whether this function is even. odd, neither . [1] (c) Find the Fourier series for this function To obtain full marks. your final answer should be simplified so that it does not contain any terms of the form cos 5 sin $ where kis an integer, [20] (d) By considering pointwise convergence of this Fourier series at t = evaluate the sum of the series ~" (5]

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