Help $\lim_{k \to \infty} \frac{1-e^{-kt}}{k}=? $ what is the lime of $ \frac{1-e^{-kt}}{k}$ as $k \to \infty$?
Is that just equal $\frac{1}{\infty}=0$?
Does any one can help, I am not sure if We can apply L'Hopital's rule. S 

HINT:
If $t=0,e^{-kt}=1$
If $t>0, \lim_{k\to\infty}e^{-kt}=0$
If $t<0, t=-r^2$(say), $\lim_{k\to\infty}\frac{1-e^{-kt}}k=\lim_{k\to\infty}\frac{1-e^{kr^2}}k=\frac\infty\infty $
So, applying L'Hospitals' rule, $\lim_{k\to\infty}\frac{1-e^{kr^2}}k=-r^2\cdot\lim_{k\to\infty}\frac{e^{r^2t}}1=-r^2\cdot\infty=-\infty$
