14.3. Conditions for Applying the Theorem

Try these first

1. 1.

   What must be true about f(t) for IVT to apply?

   Hint

   Think about the conditions needed for a function to be transformable.

2. 2.

   Why should lim t→0+ f(t) exist?

   Hint

   Consider the importance of finite values in mathematical functions.

3. 3.

   What condition must f(t) meet for IVT to be applicable?

   • Must be continuous
   • Can have impulses
   • Needs to be non-transformable

   Hint

   Consider what continuity means for functions.

4. 4.

   True or False: IVT can be applied to functions that include Dirac delta functions at t=0.

   • True
   • False

   Hint

   Think about continuity requirements.

5. 5.

   Given the function F(s) = 2/(s^2 + 3s + 2), find the initial value at t=0 and address whether IVT conditions are met.

   Hint

   Start by calculating the limit and consider how the quadratic behaves.

6. 6.

   Design a piecewise function f(t) where IVT fails, explaining the reasoning.

   Hint

   Think about what discontinuity means in relation to limits.