The appropriate Fourier series for f(x) = {1: { 1, -π< x < 0 0≤x≤ T
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FOR REVIEW PURPOSES.
Fourier Series
![f(x)
= {
-f:
The appropriate Fourier series for
2
a. f(x) = Σ=11-(-1)" sin nx
T
n
2
1-1"
⇒.f(x): = 14,00
- Σn=1
- sin nx
πT
n
=. f(x) = 2
1
d. f(x) = 2 + Σn=1 = cos nx
-π<x<0
1, 0≤x<T](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38c2618e-4acf-41c7-a022-94a725b363f8%2F79f04f46-995c-497b-9544-96c6d39f0c4f%2F4qhbedb_processed.png&w=3840&q=75)
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- Hf(x) x2; coefficient b, in this Fourier series is: f(x+4) f(x), the اختر احدى الدجابات a. 2 (-1)". COS (пп)? 2 b. (-1)" sin (пп)2 С. (-1)" (пп)? d. None of all- 2sxs-1 QI/ Find the Fourier series for the Function f(x) = 1 -15xs1 1Let /(x) = {°a- ) for 0 < x < 1, for 13x < 3. (a) Compute the Fourier cosine coefficients for f(x). ao = ak kr (b) Give values for the Fourier cosine series C(x) = a, + E, cos C(1) = C(-2) = C(4) =For the given periodic function, S(x) =} nx The coefficient a,, of the continuous Fourier series associated with the given function f(x) can be computed as an =((cos nn – 1)] The answer is a, = (cos nn – 1)| cos NT the answer is a, = (-cos nn + 1)]Suppose (m/3) = 3 and f '(m/3) = -7, and let g(x) = f(x) sinx and h(x) = (cos x)/(x). Find the following. (a) g(n/3) 3-5√3 2 (b) h'(π/3) 5-3√3 18 x x 57Find the trigonometric Fourier series for the function f(x): [-π/2, π/2] → R given by the expression: f(x) = ²2 FS(x) FS(x) = sinh n π FS(x) = FS(x)=sinh 7|1+2 2 sinh n T (-1)^ + Σn=1 n²+1 (-1)" inh 71 2n=1 n²+1 sin T π 1 + ΣΩ + -(cos 2nx (-1)" n=1 n²+1 + ΣΩ sin 2nx) -(cos 2nx + n sin 2nx) (cos 2nx n sin 2nx (-1)" (cos 2nx n+1 >] -n sin 2nx) 2nx)].Find the Complex Form of the Fourier Series for the following periodic functions (-1)" 1) f(x) =x -7f(x) = sin nx 14.b The appropriate Fourier series for 100 1-(-1)" a. f(x) = Σn=1 n πT 2 1-12 b. f(x) = ²x = Σn=1 sin nx TT n c. f(x) = 2 d. f(x) = 2 + Σ=1= cos nx n -1, 1, -πsolve using fourier seriesf(x) is periodic with period 2\pi and the picture is the graph of f(x) on [-\pi, \pi]. find the values about the Fourier series of f(x): (a) what is a (b) whenx = (c) when.x = (d) whenx = π 2 2 -T KIN -5 k KN C f(x) 2 π XCalculate the first few terms of the Fourier series of -sin(2-x), 0≤x < sin(2-x), -Q1: Find the phase angle form of the Fourier series for the function define by f(t)=4-t, 0SEE MORE QUESTIONSRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,