Question: The Laplace Transform turns a given function f = f(t) into a new function F = F(s) by way of an improper integral: F(s)

The Laplace Transform turns a given function f = f(t) into a new function F = F(s) by way of an improper integral: F(s) = e="f(t) dt. Suppose f(t)=et/2. (a) Find the set of real numbers s for which the improper integral defining F(s) converges. Answer in interval notation. Answer: (b) Find a simple formula for F(s), valid on the interval described in part (a). Answer: F(s)=

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