Capacitors under rapid current change
First, your premise is wrong. Capacitors eat di/dt for lunch. The current into the a capacitor is proportional to dv/dt, though, so high dv/dt might result in destructive current. 

An AC waveform that is continuous like a triangle wave or sine wave has a bounded dv/dt, so (if that limitation is true) the current through the capacitors is also bounded when they are connected. 

There is, however, something to worry about when the switch is closed connecting the capacitors to the AC voltage. Since this looks like homework, I think that is enough of a hint you should be able to figure it out.