I have this Laplace transform
$$B^*(s)=\frac{1-\frac{\mu }{\mu +s}}{s-\lambda +\frac{\lambda \mu }{\mu +s}}$$
and I am trying to compute the moments.
When I take the derivative and then evaluate it at $s=0$, it is not determinable. I.e.,
$$\frac{d}{ds}\left[\frac{1-\frac{\mu }{\mu +s}}{s-\lambda +\frac{\lambda \mu }{\mu +s}}\right]_{s=0} = \mbox{Indeterminate}$$
But, if I take the Inverse Laplace Transform, it exists...
$$[B^*(s)]^{-1}=e^{-t (\mu -\lambda )}$$
Question:
- How do you take the derivative of $B^*(s)$ and evaluate the result at $s=0$?