- #1

euphtone06

- 22

- 0

## Homework Statement

[tex]f(t) = e^{-m't}u(t)},

h(t) = e^{-mt}u(t)[/tex]

[tex]f(t)*h(t)[/tex]

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

## Homework 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]

## 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 don't 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]