8.1.3 - Proof of the Division by t Rule
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Practice Questions
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What is the Division by t rule?
💡 Hint: Think about how division relates to integration.
Which theorem allows us to switch the order of integration in proving the Division by t rule?
💡 Hint: Recall that it deals with iterated integrals.
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Interactive Quizzes
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What is the relationship between division by t in the Laplace domain?
💡 Hint: Consider how operations in one domain connect to those in another.
True or False: The Division by t rule can be used for any function.
💡 Hint: Think about the requirements for applying the rule.
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Challenge Problems
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Prove the Division by t Rule for the function \( e^{at} \).
💡 Hint: Start with the definition of the Laplace transform.
Apply the Division by t Rule to find the Laplace transform of a more complex function, for example, \( \frac{e^{-at}}{t} \).
💡 Hint: Use known transforms to simplify the integration process.
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