1.6 - Proof of the First Shifting Theorem
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Practice Questions
Test your understanding with targeted questions
What is the Laplace Transform of e^(2t)?
💡 Hint: Use the basic exponential Laplace Transform.
What happens to the Laplace Transform when multiplying by e^(at)?
💡 Hint: Refer to the theorem's statement.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the result of applying the First Shifting Theorem if ℒ{f(t)} = F(s)?
💡 Hint: Think about how e^(at) affects the Laplace variable.
True or False: Using the theorem, ℒ{e^(-2t)cos(t)} results in F(s + 2).
💡 Hint: Recall the correct direction of the shift.
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Challenge Problems
Push your limits with advanced challenges
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.
Find the Laplace Transform of e^(-5t)(t^3).
💡 Hint: Apply integration by parts, track using the theorem step-by-step.
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