1.9 - Common Mistakes to Avoid
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Practice Questions
Test your understanding with targeted questions
What happens to the Laplace Transform when applying to e^{-2t}f(t)?
💡 Hint: Think about how the exponential term affects the shift.
True or False: The integral converges if s < Re(a).
💡 Hint: What do we need for convergence?
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
When applying the First Shifting Theorem with e^{-4t}, what happens to s?
💡 Hint: Think about whether you are shifting left or right.
True or False: It's always okay to apply the theorem without checking s > Re(a).
💡 Hint: How does convergence affect your result?
3 more questions available
Challenge Problems
Push your limits with advanced challenges
Given the function f(t) = e^{-2t} sin(4t), calculate the Laplace Transform using the First Shifting Theorem.
💡 Hint: Start with finding the base transform then shift it.
How would you apply the theorem to calculate the Laplace Transform of e^{3t} e^{-t}cos(5t)?
💡 Hint: Ensure the shifts combine correctly.
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