Let f(x) = ex On [-∞, ∞] Part A) Show that f(x) dx Converges - Part B,) Find the Fourier integral representation of f(x)|
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![Let f(x) = ex On [-∞0, ∞]
Part A) Show that fo f(x) dx Converges
Part B,)
Find the Fourier integral representation of f(x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a87a47e-fef0-4987-bbe4-70aee2878e3d%2F4b434de2-691c-4867-8dcf-ef74fa2c38c9%2F328n9lu_processed.jpeg&w=3840&q=75)
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- Let f(x) = x - cos(™) +1_ on [−1,1] a) Use Bisection Method to find P3 (use 5-chopping digit) |P-P4| b) Approximate! mmppp.Consider the function f(x) = cos(2x) for -2pi < x ≤ 2pi and zero otherwise.A) Show that it meets the condition of having a Fourier transform.B) Find it's Fourier transform F(k).C) Demonstrate that F(0) = area under the curve of f(x).-1, -1< x < 0 1, 0< x < 1 0, otherwise The Fourier integral of f(x) =
- Solve it earlyV:53)WHAT IS THE FOURIER EXPANSION OF THE PERIODIC FUNCTION WHOSE DEFINITION IN ONE PERIOD IS : F(t) = for -IHelpThe function f(x) is defined by f(x) = 0 1- |×| for |x|≤ 2 for |x| > 2. Calculate the form of f'(x) and plot graphs of both f(x) and f'(x). Calculate directly the Fourier transforms F[f] and F[f] and confirm that F[f'] = ikF[f]. Now consider the Inverse Fourier Transform of F[f], evaluated at x = L sin² k k2 dk = π. 0, to show (1)true of false?Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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