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

Test your understanding with targeted questions related to the topic.

Question 1

Easy

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

πŸ’‘ Hint: Use the shift for e^(3t).

Question 2

Easy

What is β„’{e^(5t) * cos(t)}?

πŸ’‘ Hint: Start with the transform of cos(t).

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 β„’{e^(2t)sin(3t)}?

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

πŸ’‘ Hint: Start with the basic sin transform.

Question 2

True or False: β„’{e^(-3t)cos(4t)} = (s+3)/(s^2 + 16)

  • True
  • False

πŸ’‘ Hint: Check the parameters for the cosine function.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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

πŸ’‘ Hint: Combine the exponentials first before applying the theorem.

Question 2

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

πŸ’‘ Hint: Break down the problem into two parts first.

Challenge and get performance evaluation