Practice Common Mistakes To Avoid (1.9) - Topic 3: First Shifting Theorem

Practise this section

11 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
5 questions · about 3 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What happens to the Laplace Transform when applying to e^{-2t}f(t)?
Show hintHide hint
Think about how the exponential term affects the shift.
Question 2.
True or False: The integral converges if s < Re(a).
Show hintHide hint
What do we need for convergence?
3Question 3.
When applying the First Shifting Theorem with e^{-4t}, what happens to s?
- s + 4
- s - 4
- s
Show hintHide hint
Think about whether you are shifting left or right.
4Question 4.
True or False: It's always okay to apply the theorem without checking s > Re(a).
- True
- False
Show hintHide hint
How does convergence affect your result?
Question 5.
Given the function f(t) = e^{-2t} sin(4t), calculate the Laplace Transform using the First Shifting Theorem.
Show hintHide hint
Start with finding the base transform then shift it.
Question 6.
How would you apply the theorem to calculate the Laplace Transform of e^{3t} e^{-t}cos(5t)?
Show hintHide hint
Ensure the shifts combine correctly.

7 more questions in this section. Enroll free to practise them all.