Q1(a) Given that: f(x) = {C (Cos x, 0, os %. 0
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- A periodic function f(x) is defined by f(x) = x² + 3 for –2(b) Using the answer to Part (a) and without using Theorem 2.2.4, find the real Fourier series of the function f(x) = -2x 2r-8 if 0 < x < 2 if 2 < x < 4 and f(x+4)=f(x).for b?= 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.+3 - n2. Show that the Fourier series function defined by f(x) below is an even function. Hence determine the Fourier series for the function: f(t)= 1-1, 1+1, when - <1 <0 when 0 <11. Find the Fourier series of functions.5) a) Construct a Fourier Series for f(x) = (x² - 0x)for 0 < x < 3t b) Briefly explain the application of half – range Fourier series in your SpecializationLet f(x)={0 for 0<x<1 f(x)={−(3−x) for 1<x<3. Compute the Fourier cosine coefficients for f(x) 1. A0= 2. An= Give values for the Fourier cosine series C(x)=A02+∑n=1∞Ancos(nπ3t)C(x)=A02+∑n=1∞Ancos(nπ3t). C(1) C(−2) C(4)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,