Practice Summary - | 1. Laplace Transforms & Applications - Definition of Laplace Transform | Mathematics - iii (Differential Calculus) - Vol 1
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Practice Questions

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Question 1 Easy

What is the definition of the Laplace Transform?

💡 Hint: Look for the integral form.

Question 2 Easy

List one condition for the existence of the Laplace Transform.

💡 Hint: Think about the continuity of functions.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the Laplace Transform of a constant function f(t)=1?

1/s
s
e^-s

💡 Hint: Consider the integral limits and form.

Question 2

True or False: The Laplace Transform can only be applied to continuous functions.

True
False

💡 Hint: Think about the conditions for the transform.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the function f(t) = cos(ωt), compute its Laplace Transform.

💡 Hint: Recall integration by parts or trigonometric identities.

Challenge 2 Hard

Show that the time function f(t) = t² has the Laplace Transform F(s) = 2/s³.

💡 Hint: Use integration techniques for polynomials.

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