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What exactly is 6.2 #9 asking when it says to use another method to find the laplace transform for Prob 1? (AM, 07-Oct)

When checking my answer for 6.3 #8, the inverse laplace transform of my solution is correct for positive s however goes on for (1-e^-t) toward -infinity. Is this ok since the laplace transform only cares about positive time? Or is my solution missing something? (AM, 07-Oct)

Can anyone provide some insight on 6.3 #8? I don't understand how to work with the 1-e^-t.

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