1.11. Additional Exercise (Practice)

Try these first

1. 1.

   Find the Laplace Transform of e^(3t) * f(t) where f(t) = 1.

   Hint

   Use the shift for e^(3t).

2. 2.

   What is ℒ{e^(5t) * cos(t)}?

   Hint

   Start with the transform of cos(t).

3. 3.

   What is the result of ℒ{e^(2t)sin(3t)}?

   • 3/(s-2)^2 + 9
   • 3/(s+2)^2 + 9
   • 3/(s-2) + 9

   Hint

   Start with the basic sin transform.

4. 4.

   True or False: ℒ{e^(-3t)cos(4t)} = (s+3)/(s^2 + 16)

   • True
   • False

   Hint

   Check the parameters for the cosine function.

5. 5.

   Find the Laplace Transform of e^(5t) * e^(-2t) * sin(3t).

   Hint

   Combine the exponentials first before applying the theorem.

6. 6.

   Determine the Laplace Transform of the function e^(3t) * cos(2t) + e^(-t) * t.

   Hint

   Break down the problem into two parts first.