The Laplace transform is said to exist for a specific complex s if the magnitude of the
Chapter 9, Problem 9.56(choose chapter or problem)
The Laplace transform is said to exist for a specific complex s if the magnitude of the transform is finite-that is, if IX(s)l < oo. Show that a sufficient condition for the existence of the transform X(s) at s = so = o-o + }wo is that J +oo -oo lx(t)ie-O"ot dt < oo. In other words, show that x(t) exponentially weighted by e-CYot is absolutely integrable. You will need to use the result that, for a complex function f(t), 1 r f(t)dtl ~ r /J(t)/ dt. (P9.56-l) Without rigorously proving eq. (P9.56-1), argue its plausibility.
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