Rate of change of parameters through L and C
Let's explain by analogy:
If a car goes 50 km/h currently does not mean neccessarily that the car will ever move away 50km from where it is now (e.g. if it stops moving after 5min or if it turns back).

So if there are rates like 100A/s or 1000V/s doesn't mean that there will ever be a current of 100A or a voltages of 1000V. It is very likely that those rates become much smaller after a very short time (fractions of a second) and maybe even become nagative.