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Math Help - la place transform of t^2e^(-2t) from definition

  1. #1
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    la place transform of t^2e^(-2t) from definition

    if i try to write out what i did on this it will be very messy, but my final answer was:

    1/(s+2) - 1/((s+2)^2) - 1/((s+2)^3) , s =/= -2

    is this right?
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  2. #2
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    You should eliminate the mess and somehow lose the first two pieces.

    Do t^2 and e^(-2t) separately and get an idea of where you are aiming.
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  3. #3
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    If you are using the definition, you should know that

    .

    It's not pretty, but here you go...

    .


    Of course, it's much, much, much easier to use the fact that , because then...

    .
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  4. #4
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    thanks for that.. one question..
    why do you differenciate the first term only in the 6th line, and why is that acceptable?

    i.e when lim {ε^2/e^((s+2)ε)} goes to lim {2ε/[(2+s)e^(2+s)ε]}
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  5. #5
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    I didn't, I used L'Hospital's Rule.
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  6. #6
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    ahhhh yes i see... thanks heaps
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