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 does the First Shifting Theorem state?
💡 Hint: Remember the relationship between multiplication by e and shifting.
Question 2
Easy
If \( f(t) = t \), what is \( \mathcal{L}\{e^{3t} t\} \)?
💡 Hint: Determine the basic Laplace Transform of t first.
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 First Shifting Theorem's main result?
- \\( \\mathcal{L}\\{f(t)\\} = F(s) \\)
- \\( \\mathcal{L}\\{e^{at} f(t)\\} = F(s + a) \\)
- \\( \\mathcal{L}\\{e^{at} f(t)\\} = F(s - a) \\)
💡 Hint: Focus on the direction of the shift.
Question 2
True or False: The condition \( s > a \) must be satisfied for the theorem to apply.
- True
- False
💡 Hint: Think about the implications of the exponential function.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Derive the Laplace Transform for \( e^{2t} \cos(5t) \) using the First Shifting Theorem.
💡 Hint: Identify the base transform first, then apply the theorem.
Question 2
If \( g(t) = e^{t} \sin(t) \), find \( \mathcal{L}\{g(t)\} \).
💡 Hint: Remember to isolate the transform of \\( \\sin(t) \\) before applying the exponent.
Challenge and get performance evaluation