In order to be assured by a theorem that the Fourier Series of $f$ on $[ a , b ]$ converges to $f$ , which of the following conditions need to be satisfied? Select all that apply.
A) $f$ is continuous on $$[ a , b ]$$
B) $f ^ { \prime }$ is continuous on $[ a , b ]$
C) $f$ is piecewise continuous on $[ a , b ]$
D) $f ^ { \prime }$ is piecewise continuous on $[ a , b ]$
E) $f$ is integrable on $[ a , b ]$

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The Answer of In order to be assured by a theorem that the Fourier Series of $f$ on $[ a , b ]$ converges to $f$ , which of the following conditions need to be satisfied? Select all that apply.
A) $f$ is continuous on $$[ a , b ]$$
B) $f ^ { \prime }$ is continuous on $[ a , b ]$
C) $f$ is piecewise continuous on $[ a , b ]$
D) $f ^ { \prime }$ is piecewise continuous on $[ a , b ]$
E) $f$ is integrable on $[ a , b ]$

In Order to Be Assured by a Theorem That the Fourier