Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the Laplace Transform of \(e^{at}\)?
💡 Hint: Recall the basic property of Laplace Transforms.
Question 2
Easy
State the multiplication property when multiplying by \(tn\).
💡 Hint: Think about how differentiation affects the transform.
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 does the multiplication by \(tn\) property do to a function's Laplace Transform?
- It massifies the function.
- It shifts the function.
- It differentiates the transform \\(n\\) times with alternating sign.
💡 Hint: Focus on how multiplication affects differentiation.
Question 2
True or False: The function must be continuous everywhere for the multiplication by \(tn\) property to hold.
- True
- False
💡 Hint: Remember the conditions for the Laplace Transform.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove the general multiplication property for \(n=2\) using integration by parts.
💡 Hint: Use the integration by parts technique for differentiation.
Question 2
Given \(f(t) = e^{2t}\), find \(L\{t^3 f(t)\}\) and show all steps.
💡 Hint: Compute \\(L\\{e^{2t}\\}\\) first to establish a solid base for your derivatives.
Challenge and get performance evaluation