Q5): Determine the Fourier series of the function f(x) = 1 - x² in the interval [-1, 1].
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- Q2. Find the Fourier series for the function f(x) = ›>-6 for for 0Expand the function f(x) = X, if 0 < x < 3 6x, if 3 < x < 6 in a half-range (a) sine series; and (b) cosine series. In addition, plot what the two Fourier series converge to.Q2/ Find the Fourier series to represent the function f(x) given by: -1 for f(x) = 0 for +1 for I -H4. Express the f(x)=1+x function as a Fourier series in the interval of -TDetermine the fourier series for the periodic functionBy using Fourier series a.= an= bn= Then the Fourier series of f(x)=(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).find the Fourier series of this 2-perodic function.If f(x) = (n - x)2, find the Fourier series of period 2n in the interval (0,27) and hence evaluate+ %3D 12Recommended 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,