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Math Help - Wordy question

  1. #1
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    Wordy question

    Ok, I'm going to be honest here and say I don't completely understand what I'm being asked here.

    f(t)=3sin(t) + 5cos(3t)

    suppose that for t >= 0, the function f(t) is non-negative and that it's derivative is bounded, I.e there exists M E R such that for all t >= 0,
    |df/dt|<= M.
    Let F1(s) = Laplace{f(t)} and F2(s) = Laplace{f^2(t)} and suppose that these transforms are defined for positive values of s. Prove that there exist two constants A, B E R such that for all s >= 0 we have the following upper bound.

    F2(s) <= (1/s)(A+BF1(s))

    thank you for any help I'm really struggling on this one.

    Rodregez
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  2. #2
    MHF Contributor

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    Quote Originally Posted by Therodregez View Post
    Ok, I'm going to be honest here and say I don't completely understand what I'm being asked here.

    f(t)=3sin(t) + 5cos(3t)

    suppose that for t >= 0, the function f(t) is non-negative and that it's derivative is bounded, I.e there exists M E R such that for all t >= 0,
    |df/dt|<= M.
    Let F1(s) = Laplace{f(t)} and F2(s) = Laplace{f^2(t)} and suppose that these transforms are defined for positive values of s. Prove that there exist two constants A, B E R such that for all s >= 0 we have the following upper bound.

    F2(s) <= (1/s)(A+BF1(s))

    thank you for any help I'm really struggling on this one.

    Rodregez
    Are you sure you haven't confused two different problems here? f(x)= 3sin(t)+ 5cos(3t) is NOT "non-negative for t> 0". In particular, f(1)= 3sin(1)+ 5cos(3)= -2.4255.
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