Final Value Theorem (FVT)

Learned in MATH213.

Theorem 3: Final Value Theorem

For a function , if

  • is a proper rational function
  • has the property that all the poles have real parts that are strictly negative with the exception of a single pole (of order 1), i.e. , at

or if is the product of a function satisfying the above conditions multiplied by a complex exponential , then

If the poles of a rational function do not satisfy the above condition, then does not exist.

If the F does not satisfy those two conditions...

Then you say that the limit does not exist.