Consider the square waveform: 4 3. 2. -37 -27 -1 -2 -3. -4 -5- The function representing the above waveform, between – n and T, is described by 0. – T<æ < 0 f(x) = { | 4 0
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- Find the Fourier series for the given function. f(x) = 9 2⁰⁰ 9 2 πm=12m - f(x) = 9 - - Σ 100 9 Im=1M - 1 f(x) = 20⁰ 9 Σ πm=12m - 1 f(x): = - 200 9 Σ πm=12m 2 9 9 °ƒ(x) = ²/1 + ² £; Σ 2 πm=12m - 9|N9|N 2 -sin 1 -sin f(x) = {% (2m 1)лx L (m1)лx L (2m — 1)лx) L (2m — 1)лx - L (2m − 1)лx) L 9, L≤ x < 0, 0 ≤ x < L; ¡cos((2m. -sin 1 -7cos (12m- -COS 1 f(x + 2L) = f(x)Find the cosine Fourier coefficients for the function f(x) = 35 cos(3x), on 0Sxs. O A None of these. 140 and an- 35 (-1)+1 (-1)" 2n+3 2n-3 O B.40 =- 37 n=1,2,3,... 140 and an- 70 (-1)+1 (-1)" 2n +3 Oca0 =- 2n-3 n=1,2,3,... 140 and an= 元 70 (-1)*1 2n +3 (-1)" 2n-3 O Da0 =- n = 1,2,3,... %3D 70 (-1)+1 (-1)" 2n-3 2n+3 n= 0,1,2,3,... OE an=(a) Prove that n + 2n is divisible by 3 for each n EN. (b) Let z = sin 1 (in radians) and let y = v2. Prove that the following statement is false: (z+ y € Q) A (1- y E Q). (c) Let ai = 1 and let a2 = n. For n > 3, we define recursively an = an-2 – an-1. Is it true that a2021 is rational? Prove that your answer is correct.
- 1. Find The Fourier series for the function defined by 0can you write this out so it is clear to read and understand please• Prob.7. Find the Fourier series expansion of the function in fig. 4.15. A f(t) 4TO Fig. 4.15Consider the following. (A computer algebra system is recommended.) -23- . -3 Sxs 0, (x + 6) - (x) OThank you so much!Find the Fourier series representation of the even extension of the function ƒ(x)= Then, find the value of a0 if c = 7.7, and b = 6.6. Round off the final answer to five decimal places. ex+b Sex 4c+b if 0(a) (i) Simplify this function and plot it on the interval -2.5 ≤x≤ 2.5. (ii) Consider the periodic function defined within one period by the formula: P(x)=x+1-(x+1) it - sxs if 2 Determine whether the function is odd, even or neither. (iii) Determine the average value of the function on the period. (iv) Find coefficients of the Fourier series for this function. (V) Present the Fourier series of the function in terms of the E-notation.M3- Please I want solution of this question with all steps. ThanksRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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