Convolution Problem

1. Jan 31, 2008

euphtone06

1. The problem statement, all variables and given/known data
$$f(t) = e^{-m't}u(t)}, h(t) = e^{-mt}u(t)$$

$$f(t)*h(t)$$
Applying l'hopital's to find the result in the limit $$m' \rightarrow m$$

2. Relevant equations
$$lim_{t\rightarrow c}$$$$\frac{f(t)}{h(t)}$$ = $$lim_{t\rightarrow c}$$$$\frac{f'(t)}{h'(t)}$$

3. The attempt at a solution

$$h(t - \tau)$$ = e$$^{m\tau}$$
$$f(\tau)$$ = e$$^{-m'\tau}$$

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

$$lim_{\tau\rightarrow c}$$$$\frac{e^{-m'\tau}}{e^{m\tau}}$$ = $$lim_{\tau\rightarrow c}$$$$\frac{-m'e^{-m'\tau}}{me^{m\tau}}$$