15.6. Applications of Final Value Theorem

Try these first

1. 1.

   What does the Final Value Theorem help determine?

   Hint

   Think about the output of a system over time.

2. 2.

   What must be true for a function f(t) to use FVT?

   Hint

   Think about what 'convergence' means.

3. 3.

   What does the Final Value Theorem determine?

   • The amplitude of a wave
   • The steady-state value of a function
   • The initial value of a function

   Hint

   Consider what happens to functions over time.

4. 4.

   True or False: FVT can be applied to any function regardless of its poles.

   • True
   • False

   Hint

   Remember the conditions for FVT.

5. 5.

   Suppose you have f(t) = 4 - e^(-t/2). Calculate the final value using FVT, and explain your steps.

   Hint

   Ensure that you follow the steps methodically.

6. 6.

   Explain why FVT fails for the function f(t) = sin(t) using its properties.

   Hint

   Think about what the behavior of sin(t) is over time.