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Compute the inverse Laplace transform f(t) = L−¹[F(s)] of the following function: 1 s+o(e-as-e-bs) where a, b, and o are constants. F(s) =

Compute the inverse Laplace transform f(t) = L−¹[F(s)] of the following function: 1 s+o(e-as-e-bs) where a, b, and o are constants. F(s) =

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.5: Derivatives Of Logarithmic Functions
Problem 54E
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Compute the inverse Laplace transform f(t) = L-¹[F(s)] of the following function: 1 s+o F(s) = -as - e-bs) where a, b, and o are constants. Hint: Recall that the following property holds for translated functions L[f(t-a)H(ta)] = e-saF (s), which implies that f(t) = L-1¹[e-sa F (s)] = f(t— a)H(t − x)
Transcribed Image Text:Compute the inverse Laplace transform f(t) = L-¹[F(s)] of the following function: 1 s+o F(s) = -as - e-bs) where a, b, and o are constants. Hint: Recall that the following property holds for translated functions L[f(t-a)H(ta)] = e-saF (s), which implies that f(t) = L-1¹[e-sa F (s)] = f(t— a)H(t − x)
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