Practice Unit 1: Laplace Transforms & Applications - 1 | 3. Topic 3: First Shifting Theorem | Mathematics - iii (Differential Calculus) - Vol 1
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Unit 1: Laplace Transforms & Applications

1 - Unit 1: Laplace Transforms & Applications

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the First Shifting Theorem?

💡 Hint: Think about how an exponential affects the transform.

Question 2 Easy

Provide the condition needed for the First Shifting Theorem to hold.

💡 Hint: Consider what the Laplace Transform needs to work.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the First Shifting Theorem indicate?

It results in a vertical shift
It results in a horizontal shift
It has no effect

💡 Hint: Review what happens when functions are modified.

Question 2

True or False: The Laplace Transform of $e^{-at}f(t)$ results in $F(s + a)$.

True
False

💡 Hint: Recollect the shifting directions.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Find the Laplace Transform of $e^{2t} ext{cos}(3t)$ and explain your steps.

💡 Hint: Start from the basic Laplace transform of cos.

Challenge 2 Hard

A function $f(t) = t^3$ is affected by an exponential decay $e^{-kt}$. Determine the Laplace transform of this entire function.

💡 Hint: Recall the shifts and how the multipliers affect the base function.

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