The Fourier Coeficients of the Function $f ( x ) = x$

question 18

Multiple Choice

The Fourier coeficients of the function $f ( x ) = x$ on $[ - 1,1 ]$ are

• A) \(a _ { 0 } = - 2 / \pi , b _ { n } = 0 , a _ { n } = 0\)
• B) \(a _ { 0 } = 0 , b _ { n } = ( - 1 ) ^ { n } 2 / ( n \pi ) , a _ { n } = 0\)
• C) \(a _ { 0 } = 0 , b _ { n } = ( - 1 ) ^ { n + 1 } 2 / ( n \pi ) , a _ { n } = 0\)
• D) \(a _ { 0 } = 0 , b _ { n } = 0 , a _ { n } = ( - 1 ) ^ { n } 2 / ( n \pi )\)
• E) \(a _ { 0 } = 0 , b _ { n } = 0 , a _ { n } = ( - 1 ) ^ { n + 1 } 2 / ( n \pi )\)

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Definitions:

High Fever

An unusually elevated body temperature, often indicating an underlying medical condition or infection.

Sterile Irrigation

The process of cleaning or washing out a wound or body cavity with a fluid, specifically one that has been sterilized to avoid infection.

Safety Precaution

Measures taken in advance to prevent accidents or harm in potentially dangerous situations.

Upper Respiratory Infection

An infection affecting the upper part of the respiratory system, including the nose, throat, and bronchi, commonly known as the common cold.