Practice Additional Exercise (Practice) - 1.11 | 3. Topic 3: First Shifting Theorem | Mathematics - iii (Differential Calculus) - Vol 1
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Additional Exercise (Practice)

1.11 - Additional Exercise (Practice)

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Find the Laplace Transform of e^(3t) * f(t) where f(t) = 1.

💡 Hint: Use the shift for e^(3t).

Question 2 Easy

What is ℒ{e^(5t) * cos(t)}?

💡 Hint: Start with the transform of cos(t).

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the result of ℒ{e^(2t)sin(3t)}?

3/(s-2)^2 + 9
3/(s+2)^2 + 9
3/(s-2) + 9

💡 Hint: Start with the basic sin transform.

Question 2

True or False: ℒ{e^(-3t)cos(4t)} = (s+3)/(s^2 + 16)

True
False

💡 Hint: Check the parameters for the cosine function.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Find the Laplace Transform of e^(5t) * e^(-2t) * sin(3t).

💡 Hint: Combine the exponentials first before applying the theorem.

Challenge 2 Hard

Determine the Laplace Transform of the function e^(3t) * cos(2t) + e^(-t) * t.

💡 Hint: Break down the problem into two parts first.

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