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
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the Laplace Transform of the function e^(-at)?
💡 Hint: Use the basic definition of the Laplace Transform.
Question 2
Easy
Write the formula for L{tnf(t)}.
💡 Hint: Consider the relationship between multiplication by tn and derivatives.
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 formula for L{tn f(t)}?
- A) L{tn f(t)} = (d^n F(s))/(ds^n)
- B) L{tn f(t)} = (-1)^n (d^n F(s))/(ds^n)
- C) L{tn f(t)} = n * F(s)
💡 Hint: Consider what happens to F(s) when multiplied by tn.
Question 2
True or False: The multiplication by tn property requires functions to be continuous.
- True
- False
💡 Hint: Think about the requirements for Laplace Transforms.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Derive and compute L{t^4 e^(-5t)} using the multiplication by tn property.
💡 Hint: Remember to differentiate four times and apply the alternating signs.
Question 2
Explain how the multiplication by tn property impacts the complexity of solving differential equations in control systems.
💡 Hint: Consider why simplified equations are critical in engineering applications.
Challenge and get performance evaluation