Practice Initial Value Theorem - 14.1 | 14. Initial Value Theorem | Mathematics - iii (Differential Calculus) - Vol 1
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

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

14.1 - Initial Value Theorem

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.

Learning

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