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Convolution Problem

  1. Jan 31, 2008 #1
    1. The problem statement, all variables and given/known data
    [tex]f(t) = e^{-m't}u(t)},
    h(t) = e^{-mt}u(t)[/tex]

    Applying l'hopital's to find the result in the limit [tex] m' \rightarrow m [/tex]

    2. Relevant equations
    [tex]lim_{t\rightarrow c}[/tex][tex]\frac{f(t)}{h(t)}[/tex] = [tex]lim_{t\rightarrow c}[/tex][tex]\frac{f'(t)}{h'(t)}[/tex]

    3. The attempt at a solution

    [tex]h(t - \tau)[/tex] = e[tex]^{m\tau}[/tex]
    [tex]f(\tau)[/tex] = e[tex]^{-m'\tau}[/tex]

    I dont believe you can use the standard convolution procedures here. I am having a tough time figuring out how to apply the limit [tex]m' \rightarrow m[/tex] as well as what to do with the m' in the following

    [tex]lim_{\tau\rightarrow c}[/tex][tex]\frac{e^{-m'\tau}}{e^{m\tau}}[/tex] = [tex]lim_{\tau\rightarrow c}[/tex][tex]\frac{-m'e^{-m'\tau}}{me^{m\tau}}[/tex]
  2. jcsd
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