Practice Proof of the First Shifting Theorem - 1.6 | 3. Topic 3: First Shifting Theorem | Mathematics - iii (Differential Calculus) - Vol 1
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1.6 - Proof of the First Shifting Theorem

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the Laplace Transform of e^(2t)?

💡 Hint: Use the basic exponential Laplace Transform.

Question 2

Easy

What happens to the Laplace Transform when multiplying by e^(at)?

💡 Hint: Refer to the theorem's statement.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the result of applying the First Shifting Theorem if ℒ{f(t)} = F(s)?

  • F(s + a)
  • F(s - a)
  • F(2s)

💡 Hint: Think about how e^(at) affects the Laplace variable.

Question 2

True or False: Using the theorem, ℒ{e^(-2t)cos(t)} results in F(s + 2).

  • True
  • False

💡 Hint: Recall the correct direction of the shift.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Using the First Shifting Theorem, derive the transform for e^(3t)sin(2t).

💡 Hint: First find the transform of sin(2t) then apply the theorem.

Question 2

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

💡 Hint: Apply integration by parts, track using the theorem step-by-step.

Challenge and get performance evaluation