I'm having some troubles computing this limit. $\lim_{M\to\infty}M\left(\frac{1}{s} - \frac{e^{\frac{-s}{M}}}{s}\right)$
I know that the answer should be 1, but I can't seem to figure out the steps to get there.
Here are the steps I've tried taking:
The exponential approaches 1 as $M\to\infty$, $\lim_{M\to\infty}M\left(\frac{1}{s} - \frac{1}{s}\right)$
Simplifying the statement leaves $\lim\limits_{M\to\infty}M * 0$
Where do I go from here, or have I made a mistake above?
As a side note, this is for deriving the laplace transform of the dirac-delta function by approximating the dirac-delta function as a finite rectangular pulse starting a t=0 and ending at $t=\frac{1}{M}$ with a magnitude of M, then taking the limit as $M\to\infty$