Practice Topic 3: First Shifting Theorem - 1.1 | 3. Topic 3: First Shifting Theorem | Mathematics - iii (Differential Calculus) - Vol 1
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Topic 3: First Shifting Theorem

1.1 - Topic 3: First Shifting Theorem

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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 exponential functions influence the transforms.

Question 2 Easy

Identify a condition for applying the theorem.

💡 Hint: Check the relationship between s and a.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the result of applying the First Shifting Theorem to \( f(t) = \sin(b t) \)?

A. \\( \\mathcal{L}\\{e^{at} sin(bt)\\} = \\frac{b}{(s-a)^2 + b^2} \\)
B. \\( \\mathcal{L}\\{e^{at} sin(bt)\\} = \\frac{a}{(s+a)^2 + b^2} \\)
C. \\( \\mathcal{L}\\{e^{at} sin(bt)\\} = \\frac{b}{(s + a)^2 + b^2} \\)

💡 Hint: Recall the basic formula for sin under the shift.

Question 2

True or False: The First Shifting Theorem can only be applied when s > a.

True
False

💡 Hint: Consider the implications of the theorem's requirements.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Derive the Laplace Transform of \( e^{0.5t} * t^2 \) using the First Shifting Theorem.

💡 Hint: Start with the basic transform and replace \\( s \\) in the final result.

Challenge 2 Hard

Find a Laplace Transform for \( e^{4t} * an(t) \) using theoretical explanations.

💡 Hint: Consider the behavior of tan in Laplace transforms and apply the theorem correctly.

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Reference links

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