The Fourier Series of a Function $f$ Defined On $[ - p , p ]$

question 19

Multiple Choice

The Fourier Series of a function $f$ defined on $[ - p , p ]$ is $f ( x ) = a _ { 0 } / 2 + \sum _ { n - 1 } ^ { \infty } \left( a _ { n } \cos ( n \pi x / p ) + b _ { n } \sin ( n \pi x / p ) \right)$ where Select all that apply.

• A) \(a _ { 0 } = \int _ { -p } ^ { p } f ( x ) d x / p\)
• B) \(a _ { n } = \int _ { -p} ^ { p } f ( x ) \cos ( n \pi x / p ) d x / p\)
• C) \(a _ { n } = \int _ { - p } ^ { p } f ( x ) \sin ( n \pi x / p ) d x / p\)
• D) \(b _ { n } = \int _ { - p } ^ { p } f ( x ) \cos ( n \pi x / p ) d x / p\)
• E) \(b _ { n } = \int _ { - p } ^ { p } f ( x ) \sin ( n \pi x / p ) d x / p\)

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Definitions:

Absorption Costing

An accounting method that assigns all manufacturing costs, both variable and fixed, to products, thereby impacting the inventory valuation on the balance sheet.

Net Operating Income

The profit a company makes from its operations, calculated as total revenue minus operating expenses, excluding taxes and interest.

Variable Costing

An accounting method that only includes variable production costs—direct materials, direct labor, and variable manufacturing overhead—in product costs.

Absorption Costing

A product costing technique that adds up all manufacturing expenses — direct materials, direct labor, variable, and fixed overheads — into the comprehensive cost of the product.