14.3 - Conditions for Applying the Theorem
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Practice Questions
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What must be true about f(t) for IVT to apply?
💡 Hint: Think about the conditions needed for a function to be transformable.
Why should lim t→0+ f(t) exist?
💡 Hint: Consider the importance of finite values in mathematical functions.
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Interactive Quizzes
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What condition must f(t) meet for IVT to be applicable?
💡 Hint: Consider what continuity means for functions.
True or False: IVT can be applied to functions that include Dirac delta functions at t=0.
💡 Hint: Think about continuity requirements.
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Challenge Problems
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Given the function F(s) = 2/(s^2 + 3s + 2), find the initial value at t=0 and address whether IVT conditions are met.
💡 Hint: Start by calculating the limit and consider how the quadratic behaves.
Design a piecewise function f(t) where IVT fails, explaining the reasoning.
💡 Hint: Think about what discontinuity means in relation to limits.
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