Q: 5) Let -{2 1 Find the Fourier series of f(x). f(x) = -TAMO. 0 < r < π.
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- The Fourier series of a function f (x) defined on [-1, n] is given by 1 9 + cos x + 1 -cos 2x + 92 1 -cos 3x + 1 -cos 4x + ... 93 The value of the integral (f(x))² dxObtain complex Fourier series of f(t) = t|t| if |t| < πt Graph f(t)The Fourier series of the function is given by where Co = C₂ and b₂ f(x) ~ -Σ ~CO- n=0 [-7x if =Suppose that f(t) is periodic with period -T, 7) and has the following real Fourier coefficients: a2 = 3, аз — 3, b2 = -3, b3 = 0, ao 4, a1 = 1, b, = 2, (A) Write the beginning of the real Fourier series of f(t) (through frequency 3): f(t) = 2+cost+2sint+3cos2t-3sin2t+3cos3t+0+. (B) Give the real Fourier coefficients for the following functions: (i) The derivative f'(t) ao = , a1 = -1 , az = -6 , az = -9 b, = 2 , b2 = -6 bz = (ii) The function f(t) – 2 ao = , a1 = , az = 3 , аз — 3 b1 = 2 , b2 = -3 bz = (iii) The antiderivative of (f(t) 2) (with C 0) ao = , a1 , a2 = 3/2 , аз 1 b1 =-2 b2 = 3/2 b3 = (iv) The function f(t) + 3 sin(3t) + 3 cos(2t) ao = 2 , a1 = 1 , a2 = 6 , аз — 3 b, = 2 b2 = -3 b3 = 3 (iv) The function f(2t) an =2 , a1 , a2 3 , a3 3 b, = 2 , b2 = -3 b3 = 0Let f(e) = { , 1 ISI< 2n Find the Fourier series of f (x) over the interval [0,27]Q Find Fourier series an [o, 2w] くxく下 o f cx)= _2π-X πくx< 2π 3 fcx):I need help with these: a) Find the Fourier series of f(x) = |x| where −L < x < L. b) What is the Fourier series of the function f of period 2L defined byf(x) = -1 if −L < x< 0,f(x) = 1 if 0 < x < L,What does the series converge to when x = 0?2. Consider the function f(x) = 1 x on the interval [0, 1]. a) In two separate graphs, sketch i) the odd extension fodd on the interval [-1,1], ii) the Fourier series associated with fodd on the interval [-3,3]. b) Carefully state Fourier's theorem, including the definition of the Fourier series and the Fourier coefficients. c) Compute the Fourier coefficients of fodd and write down the Fourier series. Give full justification for your answer. d) By evaluating the Fourier series for an appropriate value of x, show that 1 2 2 2 2 3π 5TT 7π = 2|7 + +It Let f(t) be defined as f(t) = t 7L -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) = x, where - 2< x< 2 %3D determine the number to which the full fourier series of f converges at x = 2 -2 1. -42 Denote the Fourier series of f(z) = { -x, 0SEE MORE QUESTIONSRecommended textbooks for youAlgebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSON
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