In the statement of the real translation theorem, we pointed out that for the theorem to apply,…

In the statement of the real translation theorem, we pointed out that for the theorem to apply, the delayed function has to be zero for all times less than the

 

delay time. Show this by calculating the Laplace transform of the function

where to, and r are constants. (a) Assuming that it holds for all times greater than zero-that is, that it can be rearranged as

(b) If it is zero for t ≤ &-that is, that it should be properly written a

Sketch the graph of the two functions. Are the two answers the same? Which one agrees with the result of the real translation theorem?

 

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