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taxidriverhk
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Homework Statement
Let f(t) = t if 0<t<3
et 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.
Homework Equations
None
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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