In Order to Be Assured by a Theorem That the Fourier

question 25

Multiple Choice

In order to be assured by a theorem that the Fourier Series of $f$ on $[ a , b ]$ converges at $x$ , to $( f ( x + ) + f ( x - ) ) / 2$ 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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