For the given periodic function f(x) = |a|-

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For The Given Periodic Function F X A X T F X 2 F X A 5 Points Sketch F X On The Interval 31 31 1 (33.73 KiB) Viewed 24 times

For the given periodic function f(x) = |a|-<x<T f (x + 2) = f(x) (a). (5 points) Sketch f(x) on the interval [-31 31). (b). (10 points) Show that the Fourier series of f(x) satisfies 4 一 FS f(x) = (2 cos(nx)) () 2 TT n=1,3,5... 11 (c). (7 points) Based on the result of 3(b), show that T2 1+ tant 52 +z2+... 8 TE? and 공 = 1 + + 2 + + + + + + (d). (3 points) Does there exist some values of x, for which the series fails to converge to f(x)? If yes, to what values does it converge at those points? If not, justify your result.