6. (a) (b) Use integration or partial fractions to find the inverse Laplace transform of the function: 9 F(s)=- s(s²+9) Use the Laplace transform method to solve the IVP: y"+9y=18; y(0) = 0, y'(0) = 3. (Hint: Use (a) to find the solution.)

Q: 2. (a) Show that gi(t)g2(t) G₁(f) * G₂(f) where denotes convolution and gi(t) = G₁(f), 92(t)=G₂(f).…

A: We start with the time-domain signals and their Fourier transforms:Now, the convolution in the time…

Q: (Exercise 23 on page 225) Find the inverse Laplace transform of the function using the Heaviside…

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Q: The Laplace transform of x(t) is X(s). Given x(0)=2 and x'(0)=-1, write an expression for the…

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Q: The function x(t) satisfies the ODE with initial conditions x(0) = 0, x(0) = 0 and X(s) = (a) Find…

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Q: (3) A signal has Fourier transform as, 1 sinc (2w X(w) sinc + 2. Compute x(t)

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Q: Use (8), • S* f(1) dt = £^¹{F(5)}, to evaluate the given inverse transform. (Write your answer as a…

A: we know that laplace transform of e^(at) is (1/(s-a)).

Q: Q1) Find the second Taylor polynomial P₂(x) for the function f(x) = ex cos x about xo = 0.

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