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- For the given periodic function, S(x) =} nx The coefficient a,, of the continuous Fourier series associated with the given function f(x) can be computed as an =((cos nn – 1)] The answer is a, = (cos nn – 1)| cos NT the answer is a, = (-cos nn + 1)]QUESTION 2 Determine the Fourier series for f(x) = -2 when -pi < x < 0 = 2 when 0Just part D!= 1) The function f(x) periodic on the interval [0, 2л] has complex Fourier series f(x): Σ(1/n²) einx where the sum over n goes from - infinity to infinity. Convert this to cosine and sine Fourier Series by finding the values of A's and B's in the expression Ao + ΣAn cos(nx) + Σ Bn sin(nx) where each sum goes from 1 to infinity. Hint: consider the n and -n term together in the complex Fourier Series or use Euler's identity.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 Specialization! please solve (f) partRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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