7.1 - Multiplication by tn (Power of t)
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Practice Questions
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What is the Laplace Transform of \(e^{at}\)?
💡 Hint: Recall the basic property of Laplace Transforms.
State the multiplication property when multiplying by \(tn\).
💡 Hint: Think about how differentiation affects the transform.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the multiplication by \(tn\) property do to a function's Laplace Transform?
💡 Hint: Focus on how multiplication affects differentiation.
True or False: The function must be continuous everywhere for the multiplication by \(tn\) property to hold.
💡 Hint: Remember the conditions for the Laplace Transform.
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Challenge Problems
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Prove the general multiplication property for \(n=2\) using integration by parts.
💡 Hint: Use the integration by parts technique for differentiation.
Given \(f(t) = e^{2t}\), find \(L\{t^3 f(t)\}\) and show all steps.
💡 Hint: Compute \\(L\\{e^{2t}\\}\\) first to establish a solid base for your derivatives.
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