14.5 - When the Theorem Fails
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Practice Questions
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What does the Initial Value Theorem help us find?
💡 Hint: Consider its relation to Laplace transforms.
What is one condition where IVT works?
💡 Hint: Think about limits and continuity.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the Initial Value Theorem used for?
💡 Hint: Think about the application of time in the theorem.
The Initial Value Theorem fails if ___?
💡 Hint: Consider what conditions apply for the theorem to work.
2 more questions available
Challenge Problems
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Given F(s) = (s^3 + s)/(s^2 + 1), analyze via IVT and evaluate if f(0) exists. What implications arise?
💡 Hint: Focus on decomposition of terms and expected behaviors to find continuity.
Consider F(s) = 1/(s(s+1)), analyze behaviors as s approaches 0 and near poles. Discuss misinterpretations in system designs.
💡 Hint: Apply limit analysis and examine critical points of F(s).
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