For the given periodic function f(x) = |x|, - < x < f(x + 27 ) = f(x) (a). (5 points) Sketch f(x) on the interval [-31 3

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For The Given Periodic Function F X X X F X 27 F X A 5 Points Sketch F X On The Interval 31 3 1 (106.58 KiB) Viewed 19 times

For the given periodic function f(x) = |x|, - < x < f(x + 27 ) = 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 00 π 4 FS f(x) 1 #( Σου) cos(nx) 2 π n=1,3,5... (c). (7 points) Based on the result of 3(b), show that 12 1 = 00 R 1 1 1 + + 32 52 + + ... 72 를 42 +53 + 1 1 1 and alt 1 = 1 + 22 + + 32 + 52 (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.