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

    LCKurtz

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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

    LCKurtz

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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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