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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Definitions:

Cognitive Dissonance

A psychological phenomenon involving discomfort experienced by an individual who holds contradictory beliefs, values, or attitudes simultaneously.

Observable Behavior

Observable behavior refers to actions or reactions that can be visually noticed and measured by others.

Social Psychology

The examination of the way real, perceived, or suggested presence of others affects people's mental processes, emotions, and actions.

Personality Psychology

The branch of psychology focused on understanding variability in behavior and thought patterns among individuals.