Find the inverse Laplace transform f(t) = L{F(s)} of the function F(s) 5 2 s2 8 - 9 1) = c*{-(? 2 8 - .. 1A

Use the definition of the Laplace transform to find ℒ{f(t)} for f(t) = 2e^−3t Find the domain of the function F(s)

Let f(t) = e^t   if 0<=t<1              3t-7   if t >=1   Write f(t) using step function and find the laplace transform. Also, draw the graph.

Find the inverse Laplace transform f(t) = L-¹ {F(s)} of the function F(s) = = ¹{ 38 +4 {2+36} = help (formulas) ;} f(t) = L-¹, 3s + 4 s² + 36

Find the inverse Laplace transform of the following functions: (a) F(s): 3s+6 s2+3s' (b) F(s) = s2+1 s(s+1)2 · Your answer must contain detailed explanation, calculation as well as logical argumentation leading to the result. If you use mathematical theorem(s)/property(-ies) that you have learned par- ticularly in this unit, clearly state them in your answer.

Find the inverse Laplace transform of the function F(s)=s + 2/(s^2-8s+25)

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Determine the Fourier transform of f if Note : Jika = if