Practice Example 2: Non-Converging Function (Invalid Case) - 15.5.2 | 15. Final Value Theorem | Mathematics - iii (Differential Calculus) - Vol 1
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Practice Questions

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Question 1

Easy

What does the Final Value Theorem (FVT) help us find?

💡 Hint: Think about what happens to functions over time.

Question 2

Easy

Can you name a condition that must be met for FVT to apply?

💡 Hint: Consider how we classify poles.

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Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the condition for a function to be applicable under FVT?

  • Must not oscillate
  • All poles must be in the right half-plane
  • Must diverge as t approaches infinity

💡 Hint: Think about functions and their end behavior.

Question 2

True or False: The function f(t) = sin(t) can be used with FVT.

  • True
  • False

💡 Hint: Consider the behavior of the sine function over time.

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Challenge Problems

Push your limits with challenges.

Question 1

Prove that FVT does not apply for the function f(t) = cos(2t) + 2.

💡 Hint: Analyze the nature of cosine function.

Question 2

Given the function f(t) = e^(-t)cos(3t), determine whether FVT can be applied and justify your reasoning.

💡 Hint: Consider the exponential factor influencing convergence.

Challenge and get performance evaluation