Basically the continuous interest means that the infinitesimal change is the rate times what actually exists which is 0.11 * P.
The idea is that for interest if it is done on a term by term basis, then you will look at your deltas corresponding to the term. So instead of it being infinitesimal, it will be some fixed length quantity corresponding to the term (like a year, month, day, etc). When you make this delta go to zero in the limit, then you get an infinitesimal like in calculus.
Remember that in calculus the differentials represent the changes as they go to zero, but never reach zero.
In the continuous limit you get 11% of what exists which is 0.11 * P and the notion of the limit corresponds with continuous compounding.