Solution: (1) is continuous at x=0, as long as f(0+)=f(0-)=f(0)=0 When m=0, the limit values of f(0+) and f(0-) do not exist; When m ≥1:lim f (x) = 0x-> 0 because the limit of x m is equal to 0, multiplied by a number whose absolute value is less than or equal to 1, the limit value is still 0. So only m belongs to N+, that is, m is a positive integer; (2) The derivative must be continuous, so m≥ 1 is required first.