Consider the function(a) Calculate the bilateral Laplace transform of this function, using...

Consider the function

(a) Calculate the bilateral Laplace transform of this function, using definition (7.1), and give its ROC.

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(b) This function can be expressed as

f(t) = e2t[u(t + 1) – u(t – 3)].

Use tables to find its bilateral transform and its ROC.

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(c) This function can be expressed as

f(t) = e2t[u(3 – t) – u(–1 – t)]

Use tables to find its bilateral transform and its ROC.