14.7. Summary

Try these first

1. 1.

   Define the Initial Value Theorem (IVT).

   Hint

   Think about how the IVT simplifies finding initial function values.

2. 2.

   What are the necessary conditions for applying the IVT?

   Hint

   Recall the acronym LEAP.

3. 3.

   What does the Initial Value Theorem relate?

   • A function's average value.
   • The initial value of a function to its Laplace Transform.
   • The derivative of a function.

   Hint

   Think about how we evaluate functions at starting points.

4. 4.

   True or False: The limits involved in the IVT must be infinite.

   • True
   • False

   Hint

   Consider the specific conditions for the limits.

5. 5.

   Prove that if F(s) = 2/(s+5), then the initial value using IVT is correct and explain the steps taken.

   Hint

   Use the definition of the IVT and work through the substitution.

6. 6.

   Create a function whose Laplace Transform fails IVT. Explain why and calculate the limits involved.

   Hint

   Focus on the behavior around t = 0 and identify impulses.