help me to solve question number 7.8 part (c). make it into fourier series. please doing step by step so that i can know where is the answer from. and also i can solve the others question by my self. thanks ODD AND EVEN FUNCTIONS. HALF RANGE FOURIER SERIESClassify each of the following functions according as they are even, odd, or neithereven nor odd.7.8.( 20 < x< 3(a) f(x)Period = 6-2-3 < x < 0From Fig. 7-7 below it is seen that f(-x) = -f(x), so that the function is odd.f(x)-3Fig. 7-7cos x0 < x < +(b) f(x)Period = 277

Answered: Image /qna-images/answer/aa4d4bd7-2001-4dea-8096-efc9bf274902.jpg

Answered: (c) f(x) = x(10 – x), 0

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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help me to solve question number 7.8 part (c). make it into fourier series. please doing step by step so that i can know where is the answer from. and also i can solve the others question by my self. thanks

ODD AND EVEN FUNCTIONS. HALF RANGE FOURIER SERIES
Classify each of the following functions according as they are even, odd, or neither
even nor odd.
7.8.
( 2
0 < x< 3
(a) f(x)
Period = 6
-2
-3 < x < 0
From Fig. 7-7 below it is seen that f(-x) = -f(x), so that the function is odd.
f(x)
-3
Fig. 7-7
cos x
0 < x < +
(b) f(x)
Period = 27
7<x < 2n
From Fig. 7-8 below it is seen that the function is neither even nor odd.
f(z),
1
27
Fig. 7-8
(c) f(x) = x(10 – x), 0<x <10, Period = 10.
From Fig. 7-9 below the function is seen to be even.
f(x)|
25
-10
10
Fig. 7-9

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