Originally Posted by

**Lancet** In trying to get the Laplace Transform of

$\displaystyle f(t) = te^{at}$

...I end up at this step close to the end:

$\displaystyle \lim_{A \to \infty} \left[ \frac{A}{a - s} \; \frac{e^{aA}}{e^{sA}} - \frac{1}{(a - s)^2} \; \frac{e^{aA}}{e^{sA}} + \frac{1}{(a - s)^2} \right]$

I know the answer to this is

$\displaystyle \frac{1}{(a - s)^2}$

...which means the first two sets of terms equal zero. But I'm not sure I understand why. At best, the exponential fractions seem like they should converge to 1, so I'm not sure how to get to zero.

Can someone help me understand this?