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Math Help - Laplace transform of delta(t - a)

  1. #1
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    Laplace transform of delta(t - a)

    Hi all,

    I am trying to determine the laplace transform of dirac delta function,
    delta(t - a).

    I end up with:

    lim as k ---> 0 [e^(-as) -e^(-as)*e^(-sk)]/ (s*k)

    I then use L'Hopitals rule... but i can't seem to get

    lim as k--> [s*e^(-as)*e^(-sk)]/ s

    Could someone please show me how to get the above equation using L'Hopitals rule... some reason i get 2 other terms which i can't seem to cancel.

    Thanks in advance,
    ArTiCK
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  2. #2
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    Quote Originally Posted by ArTiCK View Post
    Hi all,

    I am trying to determine the laplace transform of dirac delta function,
    delta(t - a).

    I end up with:

    lim as k ---> 0 [e^(-as) -e^(-as)*e^(-sk)]/ (s*k)

    I then use L'Hopitals rule... but i can't seem to get

    lim as k--> [s*e^(-as)*e^(-sk)]/ s

    Could someone please show me how to get the above equation using L'Hopitals rule... some reason i get 2 other terms which i can't seem to cancel.

    Thanks in advance,
    ArTiCK
    Substitute into the definition for Laplace Transform and then use the sifting property of the Dirac Delta function.
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