Careful here, we're applying the limit to $sH(s)$, not $H(s)$. Then, we will be able to apply l'Hopital's rule properly. Let me know if that resolves...
Let's generalize the method I posted >>>here<<< to reflect a given point $(a,b)$ about the line $y=mx+k$, where ($m\ne0$). We will call the reflected...