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- The Fourier series of a periodic function f(x) is given 00 1 2 by 5 + 2 cos(nx) + sin( n4 n=1 The best approximation of f by a Fourier polynomial (or trigonometric polynomial) of degree 2 isProve that for any integer n NTX sin? (") dx = L. L -L Find the Fourier series of the function f(x) = sin (T) on the interval [-L, L]. Find the Fourier sine series of the function f (x) = x² cos x on the interval [-L, L]. Find the Fourier series of the function f(x) = 2L – ; on the interval [-L, L]. Denote the second Fourier cosine coefficient on the interval [-L, L] by L 27x A2 : f (x) cos -dx. -L Show that for the function f (x) = eLa 2L3 sinh(L²). A2 = L4 + A721. What is a Fourier series representation of the function (1) 2 in the range -π < x < π? f(x) = ln sec
- Q Search View Zoom Share Highlight Rotate Markup Search 2. Calculate the Fourier series up to and iIncluding the third harmonic in terms of the secondary coefficients Ao, an and b, for the periodic function defined by (4m t + 2c 0 < t < a f(1) = f(r+2x) = f(t) IConsider the function f(x)=3−x² defined in (0,1] Find its Fourier series of sines of period 2.= 1) The function f(x) periodic on the interval [0, 2л] has complex Fourier series f(x): Σ(1/n²) einx where the sum over n goes from - infinity to infinity. Convert this to cosine and sine Fourier Series by finding the values of A's and B's in the expression Ao + ΣAn cos(nx) + Σ Bn sin(nx) where each sum goes from 1 to infinity. Hint: consider the n and -n term together in the complex Fourier Series or use Euler's identity.Recommended 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,