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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A: Given integral is∫0∞t2+1t4+1dtThe integral is computed using Residue theorem as shown below.

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Q: a) Draw a graph of f(t) and determine ∫_(-∞)^∞▒|f(t)| dt  b) Write the Fourier integral…

A: Since we only answer up to 3 sub-parts, we'll answer the first 3. Please resubmit the question and…

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Q: = {H (x-2)} = √I (TTK + SCI)) H Heaviside function S→ Dirac delta function

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Q: The linear functional F: R^2[x] -> R is defined by the formula F: p -> ∫(from 1 to 0) p(t)dt.…

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Q: Q1) using Fourier transform find x(t) below x(t) = [e-3tu(t) * e-6*u(t)] dt

A: Solution is given below

Q: Let f(x) = xsin(x), −â < x < π, then a) Determine the Fourier Transform of f(x) b) Find 8 (−1)” n² -…

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Q: Let f(x) = e-x for -1 ≤ x ≤ infinity and 0 otherwise. Sketch f(x)

A: The function.To find the Fourier transform, check the condition F(0).