Let the Fourier Integral Representation of F Is $f ( x ) = \int _ { 0 } ^ { \infty } [ A ( \alpha ) \cos ( \alpha x ) + B ( \alpha ) \sin ( \alpha x ) ] d \alpha / \pi$

question 3

Multiple Choice

Let $f ( x ) = \left\{ \begin{array} { c c c } 0 & \text { if } & x < - 1 \\1 & \text { if } & - 1 < x < 1 \\0 & \text { if } & x > 1\end{array} \right\}$ . The Fourier integral representation of f is $f ( x ) = \int _ { 0 } ^ { \infty } [ A ( \alpha ) \cos ( \alpha x ) + B ( \alpha ) \sin ( \alpha x ) ] d \alpha / \pi$ , where

• A) \(A ( \alpha ) = \sin \alpha / \alpha \text { and } B ( \alpha ) = \cos \alpha / \alpha\)
• B) \[A ( \alpha ) = 2 \cos \alpha / \alpha \text { and } B ( \alpha ) = 2 \sin \alpha / \alpha\]
• C) \(A ( \alpha ) = 2 \sin \alpha / \alpha \text { and } B ( \alpha ) = 2 \cos \alpha / \alpha\)
• D) \(A ( \alpha ) = 0 \text { and } B ( \alpha ) = 2 \sin \alpha / \alpha\)
• E) \(A ( \alpha ) = 2 \sin \alpha / \alpha \text { and } B ( \alpha ) = 0\)

---

Definitions:

Merchantability

A guarantee that a product sold will meet reasonable expectations of quality and performance as implied by law.

Preassembled

Refers to items or products that are assembled at the manufacturing facility before being shipped to the customer.

Express Warranties

Explicit assurances provided by a seller to a buyer, detailing the quality, features, or specifications of the product being sold.

Brochure

A printed piece of marketing material that provides information about a product, service, or organization.