f(x) = cos (7x) for –1/2 < x < 1/2. Let the function be defined by (a) Sketch f (x) on the interval [-2,2], given that f (x + 1) = f (x)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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handwritten solution for part a 

A= 1 B = 1 C = 5
f (x) = cos (Tx) for -1/2 < x < 1/2.
Let the function be defined by
(a) Sketch f (x) on the interval [-2,2], given that f (x + 1) = f (x)
(b) Show that the Fourier series of f (x) is
(-1)"
(2n)² – 1
2
4
cos (2ntx)
-
To solve this, you can use the following similarity
2 cos A cos B = cos (A + B) + cos (A – B).
c) Use the Fourier series to calculate the sum of the series
–1)"
Š(-1)"
4n² – 1'
Transcribed Image Text:A= 1 B = 1 C = 5 f (x) = cos (Tx) for -1/2 < x < 1/2. Let the function be defined by (a) Sketch f (x) on the interval [-2,2], given that f (x + 1) = f (x) (b) Show that the Fourier series of f (x) is (-1)" (2n)² – 1 2 4 cos (2ntx) - To solve this, you can use the following similarity 2 cos A cos B = cos (A + B) + cos (A – B). c) Use the Fourier series to calculate the sum of the series –1)" Š(-1)" 4n² – 1'
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