Solution
= Solution
Let $\kappa_0=\sqrt{2mV_0}/\hbar$. As $E\to0^+$, $\kappa\to\kappa_0$ while the large denominator term scales as $1/E$. Hence
$$
\boxed{P(E)\sim\frac{4E}{V_0\sinh^2(\kappa_0a)}\longrightarrow0}.
$$
The limit is linear in incident energy for fixed positive height and nonzero width. A below-barrier wave has nonzero penetration at finite energy, but that does not imply a finite zero-energy transmitted flux.