Problem 2. For the function defined by if -22x20 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem 2.**
For the function defined by
\[
f(x) =
\begin{cases}
x - 2 & \text{if } -2 < x < 0 \\
x + 2 & \text{if } 0 < x < 2
\end{cases}
\]
Sketch the 4-period extension of \( f \) and determine the Fourier coefficients.
**Ans.**
\[
f(x) \sim \sum_{n=1}^{\infty} \frac{4}{n \pi} \left( 1 - 2 (-1)^n \right) \sin\left( \frac{n \pi}{2} x \right)
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c55fd55-ae67-4b97-a36c-91359ff73a6f%2F515aaf66-4108-4490-8924-cd6a3825f09a%2Ffkzfg6c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 2.**
For the function defined by
\[
f(x) =
\begin{cases}
x - 2 & \text{if } -2 < x < 0 \\
x + 2 & \text{if } 0 < x < 2
\end{cases}
\]
Sketch the 4-period extension of \( f \) and determine the Fourier coefficients.
**Ans.**
\[
f(x) \sim \sum_{n=1}^{\infty} \frac{4}{n \pi} \left( 1 - 2 (-1)^n \right) \sin\left( \frac{n \pi}{2} x \right)
\]
Expert Solution
Introduction
As per the question we are given a piecewise defined function f(x) with period 4 and we have to find its Fourier series expansion.
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