500uF is nonsense, possibly a statement from someone who thinks bigger numbers mean better performance.
There is no 'correct' value, the bigger it is the more low frequencies arrive at the tweeter, the lower it is, the fewer low frequencies arrive. The rate at which the volume at frequencies changes is gradual so when your tweeter says 3-15KHz it really means "don't overdrive me with low frequencies below 3KHz". In physical terms it means if you push the small speaker diaphragm too slowly and too hard it will break. The capacitor causes a gradual reduction in low frequencies that pass through it so your real objective is to pick a value that prevents too many low tones reaching the tweeter.
As I said, there is no abrupt stop in the frequencies passing through the capacitor, it is gradual so you have to pick a value that compromises stopping low frequencies but still lets enough high frequencies through. For example, if you use 3KHz as your calculation frequency and assume half level should pass at that frequency, then you want a capacitor that has a reactance equal to the tweeter impedance. Using the formula, the value that equals 4 Ohms at 3KHz is 13.26uF.
In a better filtering arrangement, the main 'woofer' speaker also has a filter, this time an inductor in series with its connection. it has the opposite effect of reducing the high frequencies and with carefully chosen values you can get a 'see-saw' effect where only the approriate frequencies reach each speaker. Going from low to high frequencies, the bigger speaker gets gradually less while the tweeter gets gradually more. Its called a 'crossover' network.
Note that 4 Ohms is the 'nominal' impedance of the loudspeaker, it will almost certainly vary wildly between 3KHz and 15KHz. The other thing you should check is the capability of your cars amplifiers to drive impedances lower than 4 Ohms. When loudspeakers are wired across each other their combined impedance becomes lower so check for example that two 4 Ohms speakers making 2 Ohms total is within the amplifiers capability. Too low an impedance can damage the amplifier.
Brian.