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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
Posted: Mon May 09, 2022 7:48 am
by answerhappygod
- 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 21 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.