1.4. Theorem Statement

Try these first

1. 1.

   Find the Laplace Transform of e^{2t} when f(t) = 1.

   Hint

   Use the theorem to shift.

2. 2.

   What is the result of the First Shifting Theorem for f(t) = t?

   Hint

   Identify the base transform first.

3. 3.

   What is the formula for the First Shifting Theorem?

   Hint

   Focus on the transformation and the shift.

4. 4.

   True or False: The condition s > a is essential for theorem application.

   • True
   • False

   Hint

   Remember the convergence aspects.

5. 5.

   Given f(t) = t^2, find the Laplace Transform of e^{3t} * t^2.

   Hint

   Start with the basic transform and apply the theorem.

6. 6.

   If f(t) = e^{-2t}sin(4t), find the Laplace Transform using the theorem.

   Hint

   Adjust for the exponential decay in sin.