Practice Key Points to Remember - 7.9 | 7. Multiplication by tn (Power of t) | Mathematics - iii (Differential Calculus) - Vol 1
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Key Points to Remember

7.9 - Key Points to Remember

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the Laplace Transform of sin(at)?

💡 Hint: Recall the basic Laplace Transform results.

Question 2 Easy

Define piecewise continuous function.

💡 Hint: Think about functions with breaks in the graph.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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

💡 Hint: Think about the relationship between time-domain functions and their transforms.

Question 2

True or False: The function must be continuous to use the multiplication by tn property?

True
False

💡 Hint: Consider the continuity requirements we've discussed.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Derive L{t·cos(at)} using the multiplication by tn property.

💡 Hint: Don't forget the alternating sign!

Challenge 2 Hard

Explain in detail the steps necessary to differentiate L{e^(st)sin(at)} in the s-domain.

💡 Hint: Refer back to the basic derivatives of exponentials.

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