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Homework Help: Existence of Laplace Transform of Piecewise Functions

  1. Dec 11, 2011 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations

    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.
    Last edited: Dec 11, 2011
  2. jcsd
  3. Dec 11, 2011 #2


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    You do???
  4. Dec 11, 2011 #3
    Sure, the limits of et and t as t approaches 3 are not equal, so f(t) should not be piece-wise continuous, isn't that right?
  5. Dec 11, 2011 #4


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    No, that isn't right. That would make the functions continuous. What is the definition of piecewise continuous given in your text?
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