Question 3 (25 points) For the given periodic function f(x) = |x|, -

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Question 3 25 Points For The Given Periodic Function F X X X T F X 2 F X A 5 Points Sketch F X On 1 (39.86 KiB) Viewed 14 times

Question 3 (25 points) For the given periodic function f(x) = |x|, -<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 TT FS f(x) = a + - 2 6 cos nx)) ( 2 TT n=1,3,5... (c). (7 points) Based on the result of 3(b), show that 1 = 1 + 32 + + 8 2 + ... 22 + + 2 32 + x + 2 + ... TT2 and = 1 + 22 (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.