Answer to Question #251959 in Calculus for JaytheCreator

Question

Expand each of the following functions in a Fourier sine series then a Fourier cosine series on the prescribed interval.

(i) 𝑓(𝑥) = 𝑒^−𝑥 ; 0 < 𝑥 < 1,

(ii) 𝑓(𝑥) = { 𝑥 0 < 𝑥 < 𝑙/2 𝑙 − 𝑥 𝑙/2 < 𝑥 < 𝑙 ; 0 < 𝑥 < 𝑙,