Practice Key Points To Remember (7.9) - Multiplication by tn (Power of t)

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6 sample questions

Question 1.
What is the Laplace Transform of sin(at)?
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Recall the basic Laplace Transform results.
Question 2.
Define piecewise continuous function.
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Think about functions with breaks in the graph.
3Question 3.
What does multiplying a function by t in the Laplace Transform do?
- It increases the order of the polynomial
- It shifts the function vertically
- It differentiates the Transform
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Think about the relationship between time-domain functions and their transforms.
4Question 4.
True or False: The function must be continuous to use the multiplication by tn property?
- True
- False
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Consider the continuity requirements we've discussed.
Question 5.
Derive L{t·cos(at)} using the multiplication by tn property.
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Don't forget the alternating sign!
Question 6.
Explain in detail the steps necessary to differentiate L{e^(st)sin(at)} in the s-domain.
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Refer back to the basic derivatives of exponentials.

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