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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the Laplace Transform of e^(2t)?
💡 Hint: Use the basic exponential Laplace Transform.
Question 2
Easy
What happens to the Laplace Transform when multiplying by e^(at)?
💡 Hint: Refer to the theorem's statement.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the result of applying the First Shifting Theorem if ℒ{f(t)} = F(s)?
- F(s + a)
- F(s - a)
- F(2s)
💡 Hint: Think about how e^(at) affects the Laplace variable.
Question 2
True or False: Using the theorem, ℒ{e^(-2t)cos(t)} results in F(s + 2).
- True
- False
💡 Hint: Recall the correct direction of the shift.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Using the First Shifting Theorem, derive the transform for e^(3t)sin(2t).
💡 Hint: First find the transform of sin(2t) then apply the theorem.
Question 2
Find the Laplace Transform of e^(-5t)(t^3).
💡 Hint: Apply integration by parts, track using the theorem step-by-step.
Challenge and get performance evaluation