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Find the Maclaurin series for cos(x) using the Maclaurin series for sin(x).
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- Use the Maclaurin series for sin(x) to compute 9 sin(2°) correct to five decimal places. 9 sin(2⁰) =Investigate Taylor series expansion. Explain how the Taylor series is used in your calculator to compute values of functions such as sin(x) , cos(x) , and ex , where x represent any value. Write a brief report explaining your findings, and give examples.By using Fourier series a.= an= bn= Then the Fourier series of f(x)=
- (*) Find the Fourier cosine series of f(x) = sin(4x) on [0, π]. Could you guess what the Fourier cosine series of sin(8x) would be?Sketch the odd periodic extension and find the Fourier Sine Series of the function given by 0Use the Maclaurin series for sin(x) to compute 6 sin(2°) correct to five decimal places. 6 sin(2°)=(a) State the Maclaurin series for sin(r) and cos(r). You do not have to derive these. (b) Using series multiplication [as in example 13, 11.10] find the power series representation of the product, sin(r) cos(r) (c) Note that sin(2x) = sin(r) cos(r). Find the Maclaurin series for sin(2r) by modifying the known series for sin(x) that you stated in part (a). Does your answer match that of part (b)? (d) Use division of power series to find the Maclaurin series for tan(r).The Fourier sine series of the function is given by where b₂ f(x) = = (3x if 05) Find the Maclaurin series for sin X. By using it, show sin X lim that as X - 0 equals 1.For the function (х 0 <х< 1 f (x) = G (1 1Assume that sin(x) equals its Maclaurin series for all x. Use the Maclaurin series for sin (8x²) to evaluate the integral 0.65 [065 sin (8x²) dx. Your answer will be an infinite series. Use the first two terms to estimate its value. Enter a mathematical expression [more..]The Fourier sine series of the function is given by where f(x) = { bn 3x if 0Recommended textbooks for youCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSONCalculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage LearningCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSONCalculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning