Problem 4. (. Recall that the convolution of f and g is defined as (S * 9)(t) = 1(2 f(P)g(t – p) dp. Let f(t) = e-2t and g(t) = e". • Evaluate the integral to find the expression for f *g and take the Laplace transform of this expression. Verify that C{f * g} that you found is equal to L{f}L{g}.

Q: Prove that for a constant function f(t)= C, the Laplace transform can be given as. F(s)= Z C= S

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Q: When calculing the Laplace transform of the function f(t)=e^2t.sin(4t) is obtained as a result:

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Q: 9. Show the Complex Fourier Integral Transform (Fourier transform) of the function defined below…

A: Given : The Complex Fourier Integral Transform (Fourier Transform) of the function is defined as :…

Q: 3) Determine the inverse Laplace Transform. where f = L{F}. 4 F(s) = In s- 3, %3D

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Q: 4. Using the definition, not the table, find the Laplace transform of (a) f(t) = −3 (b) g(t) = 4t…

A: Laplace transform of the function

Q: If the ratio of boys to girls in tennis camp is 3:5 if there are 64 campers, how many are girls 

A: We find out how many girls as follows:  • We first need to determine the total number of parts in…

Q: S(1) = >1

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Q: 5. f(t) = 3e -3* (4cos5t – 3sin7t) 6. f(t) = 3(2 – 2e-at)

A: 5)  Given function , ft=3e-3t4cos5t-3sin7t . . .(1) We use some formulae Laplace transform:…

Q: Find the inverse Laplace transform L-1{F(s)} of the function 6 F(s) = (s – 1) NOTE: The answer…

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Q: 2. Determine the Laplace transform of the following functions. Here you may use common identities…

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Q: If the Fourier transform of f(x) is f(k): f(x) x (a) Find the Fourier transform of in terms of f(k).…

A: Given that the Fourier transform of  is .We need to find the Fourier transform of  in terms of .We…