Practice Initial Value Theorem - 14.1 | 14. Initial Value Theorem | Mathematics - iii (Differential Calculus) - Vol 1
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Initial Value Theorem

14.1 - Initial Value Theorem

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Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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?

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

Determine why the IVT fails for F(s) = e^(-s)/(s + 1) in computing f(0).

💡 Hint: Evaluate the limits carefully.

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