Find Price Elasticity of Demand for p = 0
The Answer can be found in the comments by user brunosalcedo:

"Remember that elasticity measures percentual rates of change. How does q change per unit of percentual change of p? If $p=0$, then any percentual change of p results in no change at all because 0 multiplied by any number is 0. The elasticity is not just 0 at p=0, it is also continuous at $p=0$. If you compute the elasticity for small but positive prices, and then take the limit as p goes to 0, the limit is 0."