In Order to Be Assured by a Theorem That the Fourier

question 13

Multiple Choice

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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Definitions:

Behaviorist Perspective

A theory of learning based on the idea that all behaviors are acquired through conditioning, emphasizing observable behaviors over internal states.

Learning Perspective

A psychological approach that emphasizes the role of environmental influences on observable behavior.

Biological Perspective

An approach in psychology that examines psychological issues through the lens of biological processes, including genetics and brain functions.

Social Psychologists

Scientists who study how people's thoughts, feelings, and behaviors are influenced by the actual, imagined, or implied presence of others.