(a) If f(x) is an even function on the interval [–7, 7), prove that the (trignometric) Fourier series is given by f(x) ~ ao + an cos(nx).
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- Find the trigonometric Fourier series for the square 2n-periodic wave defined on the interval [-11,1]: f(x) = {0, if-SX<0 f(x) = {1, if 02. Find the Fourier series for the function f(x)= (n – x)² in -nFind the trigonometric Fourier series for the function f(x): [-T/2, π/2] → R given by the expression: ƒ(2) - {0 = O о O O cos 2x if x = [-π/2, 0] 0 if x = (0, π/2] O ∞ FS(x) = -2 cos(2x) + 1 n=1 FS(x) = −cos(2x) + Σ2 FS(x) = −sin(2x) + Σn=2 FS(x) = cos(2x) + Σn=0 FS(x) = cos(2x) + Ex-1 - n² cos² (n²-1)π 2n cos² n cos² (=) 2 n cos² (n²-1)T (+) 2 2(n²-1)π NE (+) (n.²-1) 2n cos² * ( =) 2 (n²+1)π -sin(2nx). -sin(2nx). -sin(nx). sin(2nx). -sin(2nx).(2) Find the full Fourier series for the periodic function f : R → R defined by f(x) = 1+ |x| on the interval (-1,1) and then extended using f(x+ 2) = f(x) for all r.Consider f(t)=9+2t+6t², for -If f(x) is an even function on [-pi, pi], then the Fourier series of f is of of the form a0 + E-1 a, cos(jx) 2 A True В FalseRecommended 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,