1.2 - Conditions for Existence (Dirichlet Conditions)
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Practice Questions
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What does piecewise continuity mean?
💡 Hint: Think about the continuity of the function.
State the Dirichlet Conditions.
💡 Hint: Consider which two major conditions we discussed.
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Interactive Quizzes
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What is a requirement for a function to possess a Laplace Transform?
💡 Hint: Look back at the first condition we discussed.
True or False: A function growing faster than e^(2t) can be transformed using Laplace.
💡 Hint: Recall the defining rules about growth.
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Challenge Problems
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Evaluate if the function f(t) = { 3t for 0 ≤ t < 5; t^2 - 10 for t ≥ 5 } meets the Dirichlet Conditions.
💡 Hint: Analyze the function parts for continuity and check against the nature of growth.
Given f(t) = sin(t) + e^(t^2), determine if it is suitable for Laplace Transform and explain.
💡 Hint: Consider the rapid increase of e^(t^2) compared to its constant multiplicative limits.
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