15.5.2. Example 2: Non-Converging Function (Invalid Case)

Try these first

1. 1.

   What does the Final Value Theorem (FVT) help us find?

   Hint

   Think about what happens to functions over time.

2. 2.

   Can you name a condition that must be met for FVT to apply?

   Hint

   Consider how we classify poles.

3. 3.

   What is the condition for a function to be applicable under FVT?

   • Must not oscillate
   • All poles must be in the right half-plane
   • Must diverge as t approaches infinity

   Hint

   Think about functions and their end behavior.

4. 4.

   True or False: The function f(t) = sin(t) can be used with FVT.

   • True
   • False

   Hint

   Consider the behavior of the sine function over time.

5. 5.

   Prove that FVT does not apply for the function f(t) = cos(2t) + 2.

   Hint

   Analyze the nature of cosine function.

6. 6.

   Given the function f(t) = e^(-t)cos(3t), determine whether FVT can be applied and justify your reasoning.

   Hint

   Consider the exponential factor influencing convergence.