If f(x) = x for 0 < x < n/2 and f(x) = a – x for 1/2 < x < n, show that the cosine series for this function is cos 2(2n – 1)x (2n – 1)² 2 f(x)= -- 4 T 1.
If f(x) = x for 0 < x < n/2 and f(x) = a – x for 1/2 < x < n, show that the cosine series for this function is cos 2(2n – 1)x (2n – 1)² 2 f(x)= -- 4 T 1.
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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Step 1
Given that,
Here, is defined on the interval, .
In this case and hence the cosine series has the form,
Also, by definition,
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