Answer Happy

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

Posted: Mon May 09, 2022 11:02 am

by answerhappygod

Question 3 25 Points For The Given Periodic Function F X X T X Tt F X 2 F X A 5 Points Sketch F X O 1 (66.89 KiB) Viewed 21 times

Question 3 (25 points) For the given periodic function f(x) = |x|, -T<x<TT 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 00 TC FS f(x) = 7 x -cos(nx) ) TT n=1,3,5... (c). (7 points) Based on the result of 3(b), show that 112 = + + 8 = 1+ + +2 +... +53 + ... | T12 and = 1 + + 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.