Equal to s-> The value of sF(s) at infinity, where F(s) is the frequency domain decomposition of f(t), s->; Infinity means jw-& gt；; Infinity, that is, infinite frequency, infinite frequency, should mean that it is difficult to determine. So the first meaning expressed by the initial value theorem should be that the first value of the function f is difficult to determine.
This is consistent with our normal intuition: we are not sure what will happen to anything new. One of the greatness and charm of science is that it can express this indescribable intuition with rigorous mathematics. It can be seen that if the zero point of SF(s) is less than the pole, then the first value should approach 0, that is, it is relatively small, and vice versa.
Look at the final value theorem again. The final value theorem shows that when time tends to infinity, the value of function F is equal to S->; The value of sF(s) at 0. s-& gt； 0 represents w-> 0，w-& gt； 0 means that the frequency tends to 0, that is, the value of the function f tends to be constant. Then the final value theorem should mean that no matter how the function f (which can represent anything) changes at the beginning.
But with the infinite passage of time, it will eventually return to peace. As for the final value, it can be analyzed by the number of zero poles as before.
Therefore, the initial value theorem shows that the first value of the function f is difficult to determine and there are infinite possibilities. The final value theorem (infinite frequency) shows that no matter how the function f changes at first, it will eventually return to calm with the infinite passage of time. (frequency is 0)