Suppose you're given the following Fourier coefficients for a function on the interval [-,]: a = 1, ak Fourier approximations to the Fourier series ao +(a, cos(nx) + b₂ sin(nx)). n1 Fo(z) = F₁(z) = F₂(x) = F3(x) = 0 for k ≥ 1, and bk = 2(-1)+1 for k > 1. Find the following
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- Find the inverse transform of the equation below. V(s) = (1-3s) / (s^2+8s+21) [(13*sqrt(5)/5)*sin(sqrt(5)t)*e^(-4t)] - A [3*cos(sqrt(5)t)*e^(4t)] [(13*sqrt(5)/5)*sin(sqrt(5)t)*e^{-4t)] - В [3*cos(sqrt(5)t)*e^{-4t)] [(13*sqrt(5)/5)*sin(sqrt(5)t)*e^(4t)] - [3*cos(sqrt(5)t)*e^{(4t)] [(13*sqrt(5)/5)*sin(sqrt(5)t)*e^(-4t)] + D [3*cos(sqrt(5)t)*e^(-4t)] [(13*sqrt(5)/5)*cos(sqrt(5)t)*e^(-4t)] - E [3*sin(sqrt(5)t)*e^(-4t)] [(13*sqrt(5)/5)*sin(sqrt(5)t)*e^(4t)] - F [3*cos(sqrt(5)t)*e^(-4t)]Find the Fourier transform +00 F(@) = | f(t)exp(iwt)dt of the function 0, t 0. You might want to use that +00 1 exp(iox")dx =exp (iOE! please solve (c) part
- Q4/ Choose the correct option represents the following Fourier series f(x) = x +n . T+2sinx-sin2x+2/3 sin3x-2/4 sin4x+... 3m + 2sinx – sin2x + sin3x -sinax + O Option 1 O Option 2 -2n + 2sinx - sin2x +sin3x –- sin4x + Option 3 O No one1 Find Fourier cosine transform of f(x) =< -1 0What is the substitute of the expression (9+x²)³/2 dx if f (9 +x²)3/2 method? is transform by trigo substitutionf(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, -π1. Express f(x) by the Fourier series where f(x)= {, 2, -7! please solve (f) partRecommended 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,