Practice Laplace Transforms & Applications - 8 | 8. Division by t (Inverse of Multiplication by s) | Mathematics - iii (Differential Calculus) - Vol 1
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Laplace Transforms & Applications

8 - Laplace Transforms & Applications

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define the division by t property in Laplace transforms?

💡 Hint: Think about the relationship between time domain operations and algebraic manipulations.

Question 2 Easy

What is the integral representation for division by t?

💡 Hint: Look for how the integral relates to F(s).

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the division by t property in Laplace transforms translate to?

A) Differential Equations
B) Integration in s-domain
C) Algebraic Manipulations in Time Domain

💡 Hint: Recall the fundamental concept of linking operations in both domains.

Question 2

True or False: The division by t rule can be applied to any function f(t).

True
False

💡 Hint: Look back at the conditions required for the application.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove the division by t rule using Laplace Transform properties and Fubini's Theorem.

💡 Hint: Ensure you understand each property relevant to Fubini's theorem.

Challenge 2 Hard

Evaluate ℒ{f(t) = e^(bt)sin(at)/t} using the division by t rule and simplify.

💡 Hint: Look at how both coefficients interact in the integral.

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