(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let f(t) = t if 0<t<3

e^{t}if t>3

a. Is f(t) piece-wise continuous?

b. Is f(t) of exponential order α? Either prove it by producing an M, T and α that satisfies the definition, or show that no such constants exist.

c. Does the Laplace transform of f(t) exist? Briefly explain your answer.

2. Relevant equations

None

3. The attempt at a solution

I know it is not piecewise continuous already.

But can this point prove that the Laplace transform of this function does not exist?

Or do I still have to prove if it is of exponential order α? But I don't know how to find the M, α and T

Hope anyone can help me, thank you so much.

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# Existence of Laplace Transform of Piecewise Functions

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