Let f(x) = 1 - 2x where 1 0 ≤ x ≤ Expand f(x) to a 4 Fourier sine series converging to 1 f(x) on the interval 0 ≤ x ≤ ia

The Fourier series of the function is given by where Co = C₂ and b₂ f(x) ~ -Σ ~CO- n=0 [-7x if =

Q/Determine the Fourier expansions of the periodic functions whose definitions in one period are: f1 + t 7 f(t) = -1

(Hint In part d) using the Fourier series of this problem together with simple algebra, Note that we are shortly going to prove the fact that if ∑|f^(n)|<∞∑|f^(n)|<∞ then the Fourier series of ff converges uniformly to ff. You may use this fact in your solution.)