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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the initial value of f(t) if F(s) = 3/(s + 1)?
💡 Hint: Evaluate lim (s→∞)[3s/(s + 1)].
Question 2
Easy
List one condition for applying the Initial Value Theorem.
💡 Hint: Think about the requirements needed for the theorem.
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 Initial Value Theorem state about f(t) and F(s)?
- a) lim(t→0+) f(t) = 0
- b) lim(t→0+) f(t) = lim(s→∞) sF(s)
- c) lim(s→0) F(s) = f(0)
💡 Hint: Focus on the relationship between limits involving f(t) and F(s).
Question 2
True or False: The Initial Value Theorem can be used with functions that contain impulse functions.
- True
- False
💡 Hint: What happens to the function's continuity?
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Apply the Initial Value Theorem to find the initial value of f(t) for F(s) = 6/(s^2 + 3s + 2).
💡 Hint: Simplify the expression before taking the limit.
Question 2
Determine why the IVT fails for F(s) = e^(-s)/(s + 1) in computing f(0).
💡 Hint: Evaluate the limits carefully.
Challenge and get performance evaluation