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Q: How be came? W412 431/ 3 1+ w²+2 0.4w 4-w² = 0, (w² + 2) (4 w²) + 0.4w² = 0, - w4 - 2.4w² - 8 = 0.
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![Find the first four non-zero terms of the Maclaurin series for f(x) = sin(x5) cos(x5).
f(x) =
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- Consider the expansion y = p=0 96pxop with coefficients given by a6p = (-1)Pao/(2p)!. Which function does this series correspond to? ao exp(x6). Cao sin(x). ao sin(x³). Cao cos(x6). Cao exp(x3). ao cos(x³).3. Determine the half-range sine series for the function defined by: x, 013.) Find a power series for the function f(x) = = 5 2-6x3*Q 1. Find the Maclaurin series of the given function : (a) f(x) = e=x² (b) f(x) = x³ cos(x²), c = 1 (c) f(x)= sin 3x (d) f(x) = xe", c = }, Let f(x) = cos (2x²) - 1 x² -. Evaluate the 10th derivative of fat x = 0. f(¹0) (0) = Hint: Build a Maclaurin series for f(x) from the series for cos(x).1. You are given that tan-1x = x -x3 + x7 + .- for |x| < 1. 1. | ... 3 5. Use the given series to obtain a power series for tan-(x²). b) Use the first three nonzero terms of your series in part (a) to find an 0.5 approximate value tan-1(x²) dxLet f(x) = cos (4x³) - 1 x5 Evaluate the 7th derivative of f at x = 0. f(7) (0) = 0 Hint: Build a Maclaurin series for f(x) from the series for cos(x).Answer the following points i. Find the first three nonzero terms of Maclaurin series for the functions f(x) = e* and other function f(x) = ex ii. By depending on point (i), find the series for function f(x) = Cosh(x) where ex +e-x Cosh(x): Ans./ i) ex 2 1Q1. Find (i) the Fourier cosine series and (ii) the Fourier sine series of the function f(x) = x, 0SEE MORE QUESTIONSRecommended 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