(a) Write the Fourier expansion of f(x) on [-1, and show that this series converges to...

 

Transcribed Image Text:

(a) Write the Fourier expansion of f(x) on [-1, and show that this series converges to f(x) on (-7, 7). (b) Show that the integral of f(x) can be obtained as a term-by-term integral of the Fourier series and use this to obtain a Fourier expansion of Sif(1) dt. (c) Check the result of (b) by computing f f(t) dt and expanding this function in a Fourier series on [-n,7]. 7- JT, T Let 0. f(x) = for -n <x< 0, for 0 < x <T. (a) Write the Fourier expansion of f(x) on [-1, and show that this series converges to f(x) on (-7, 7). (b) Show that the integral of f(x) can be obtained as a term-by-term integral of the Fourier series and use this to obtain a Fourier expansion of Sif(1) dt. (c) Check the result of (b) by computing f f(t) dt and expanding this function in a Fourier series on [-n,7]. 7- JT, T Let 0. f(x) = for -n <x< 0, for 0 < x <T.