Consider the function 1-х їв окны 1 if 12x22 f(x) = a) Plot the function 6). Plot its odd- Periodic and even - periodic extension over (-6,6). c) Complute its Fourier cosine and sine expansions. d). Plot the functions to which the Fourier cosive and Fourier Sine expansions Converge to.
Consider the function 1-х їв окны 1 if 12x22 f(x) = a) Plot the function 6). Plot its odd- Periodic and even - periodic extension over (-6,6). c) Complute its Fourier cosine and sine expansions. d). Plot the functions to which the Fourier cosive and Fourier Sine expansions Converge to.
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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![### Consider the Function
\[
f(x) =
\begin{cases}
1-x & \text{if } 0 < x \leq 1 \\
1 & \text{if } 1 < x < 2
\end{cases}
\]
### Exercises
a) **Plot the function.**
b) **Plot its odd-periodic and even-periodic extensions over the interval (-6, 6).**
c) **Compute its Fourier cosine and sine expansions.**
d) **Plot the functions to which the Fourier cosine and Fourier sine expansions converge.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c55fd55-ae67-4b97-a36c-91359ff73a6f%2F5a134e7f-aad7-4914-b58b-b43129902a4d%2F2g6y74h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Consider the Function
\[
f(x) =
\begin{cases}
1-x & \text{if } 0 < x \leq 1 \\
1 & \text{if } 1 < x < 2
\end{cases}
\]
### Exercises
a) **Plot the function.**
b) **Plot its odd-periodic and even-periodic extensions over the interval (-6, 6).**
c) **Compute its Fourier cosine and sine expansions.**
d) **Plot the functions to which the Fourier cosine and Fourier sine expansions converge.**
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