(III) Find the Half-range Sine series of f(x) = sin(x) on (0,2).
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- For f(x) = |x| find the coefficients from the Fourier series of f(x) on the interval (-n,1) by using the appropriate cosine or sine series.Q1// Find the Fourier series of the periodic function f(x) = cos (x +), - < x < ! 2Q1) Find the half-range sine series for the function f(t) = πt - t², in the interval 0cos (6x2 Let f(x) 1 Evaluate the 10th derivative of f at x = 0. x2 f(10) (0) = Hint: Build a Maclaurin series for f(x) from the series for cos(æ).Let f(x) be the function which is represented by the power series : f(x)= En=1 (-1)"(x-2)" Find the 5th derivative of f(x) at x = 1What is the power series represntation for the function f(x)=cos(x/3)?(7) a) Differentiate term by term to find f'(x) for the series f(x)=2 and express the n! n=0 function as a power series. b) Compare the function and its derivative; what do you notice?f(x) = |sin(x)| Find the Fourier Periodic in the range -n4 A function f(x) is defined by f(x) = π-x f(x+2π)=f(x). Express the function (a) as a half-range cosine series (b) as a half-range sine series. 0SEE MORE QUESTIONSRecommended textbooks for youCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning