Practice Common Mistakes to Avoid - 1.9 | 3. Topic 3: First Shifting Theorem | Mathematics - iii (Differential Calculus) - Vol 1
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Common Mistakes to Avoid

1.9 - Common Mistakes to Avoid

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What happens to the Laplace Transform when applying to e^{-2t}f(t)?

💡 Hint: Think about how the exponential term affects the shift.

Question 2 Easy

True or False: The integral converges if s < Re(a).

💡 Hint: What do we need for convergence?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

When applying the First Shifting Theorem with e^{-4t}, what happens to s?

s + 4
s - 4
s

💡 Hint: Think about whether you are shifting left or right.

Question 2

True or False: It's always okay to apply the theorem without checking s > Re(a).

True
False

💡 Hint: How does convergence affect your result?

3 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the function f(t) = e^{-2t} sin(4t), calculate the Laplace Transform using the First Shifting Theorem.

💡 Hint: Start with finding the base transform then shift it.

Challenge 2 Hard

How would you apply the theorem to calculate the Laplace Transform of e^{3t} e^{-t}cos(5t)?

💡 Hint: Ensure the shifts combine correctly.

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