A normal speaker can handle a lot of frequencies usually in the region from 50 hz to around 20 Khz. This also depend on the type of speaker used as larger speakers handle bass notes better then their counter smaller speakers, the latter however can handle high frequencies better than lower ones. This is the main reason that usually there will be 3 speakers in a speaker box as each speaker can handle a range of frequencies suited to its size and construction. The crossover takes care to distribute the right frequency range for each speaker.
The human ear cannot hear more than 20Khz and this will be when you are still young, As you grow older it will be more or less up to 15Khz at the most.