H.W: Find the Fourier series for the following periodic functions 1) f(x) = 2t 0

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H.W: Find the Fourier series for the following periodic functions
1) f(x) = 2t
0<t<2
f(t+2) = f(t)
2) f(x) = |t|
f(t +2n) = f(t)
3) f(x) = { 1 ²
f(t+2n) = f(t)
4) f(x) = {²₁
5) f(x) = {
6) f(x)=x, 0<x< 1,
7) f(x)=x², 0<x<2π,
8) f(t) = sint, 0<t<n,
9) f(t) = cost ,0 <t<n,
"<t <π
-T<x<0
0<x<π
-2<x<0
0<x<2
-2<x<0
0<x<2
-π<x<0
0<x<n
10) f(x) = { ²₂
0<x<π
11) f(x) = {Sinx
0
0<x<2
12) f(x) = |x|,-" <x<T
13) f(x)=x²-2<x<2
14) f(t) = sint, -n<t<n
15) f(t) = cost,-n <t <n
Transcribed Image Text:H.W: Find the Fourier series for the following periodic functions 1) f(x) = 2t 0<t<2 f(t+2) = f(t) 2) f(x) = |t| f(t +2n) = f(t) 3) f(x) = { 1 ² f(t+2n) = f(t) 4) f(x) = {²₁ 5) f(x) = { 6) f(x)=x, 0<x< 1, 7) f(x)=x², 0<x<2π, 8) f(t) = sint, 0<t<n, 9) f(t) = cost ,0 <t<n, "<t <π -T<x<0 0<x<π -2<x<0 0<x<2 -2<x<0 0<x<2 -π<x<0 0<x<n 10) f(x) = { ²₂ 0<x<π 11) f(x) = {Sinx 0 0<x<2 12) f(x) = |x|,-" <x<T 13) f(x)=x²-2<x<2 14) f(t) = sint, -n<t<n 15) f(t) = cost,-n <t <n
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