Bulk capacitors/charge reservoir for large pulse current/current exceeding supply?
Q=CV and differentiating I = C dv/dt so, if the rate of change of output voltage (due to discharge) across the capacitor is limited to (say) 0.1 volts in 5 seconds then: -

300 mA x 5 / 0.1 = C or C = 15 farads.

A 15 farad capacitor charged to (say) 5 volts, will drop to 4.9 volts after 5 seconds of supplying 300 mA to a load.

If the battery can supply 200 mA of that current then the capacitor only needs to supply 100 mA and this makes the capacitor smaller in value.

I'm sure you can now do the math for the 2A/200us example.