Practice Proof Of The Division By T Rule (8.1.3) - Division by t (Inverse of Multiplication by s)

Practice: Proof of the Division by t Rule

Lesson 8.1.3Division by t (Inverse of Multiplication by s)

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6 sample questions

Question 1.
What is the Division by t rule?
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Think about how division relates to integration.
Question 2.
Which theorem allows us to switch the order of integration in proving the Division by t rule?
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Recall that it deals with iterated integrals.
3Question 3.
What is the relationship between division by t in the Laplace domain?
- Multiplication by s
- Integration
- Differentiation
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Consider how operations in one domain connect to those in another.
4Question 4.
True or False: The Division by t rule can be used for any function.
- True
- False
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Think about the requirements for applying the rule.
Question 5.
Prove the Division by t Rule for the function $e^{at}$ .
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Start with the definition of the Laplace transform.
Question 6.
Apply the Division by t Rule to find the Laplace transform of a more complex function, for example, $\frac{e^{-at}}{t}$ .
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Use known transforms to simplify the integration process.

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