1.6 - Properties of Laplace Transform (To Be Explored in Later Sections)
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Practice Questions
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What does linearity in Laplace Transform imply?
💡 Hint: Think about how you might combine functions in algebra.
State the Initial Value Theorem.
💡 Hint: Consider what happens to F(s) at 's' approaches infinity.
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Interactive Quizzes
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What is the property that allows the transformation of linear combinations of functions?
💡 Hint: Consider the term that describes linear functions.
True or False: The Final Value Theorem can help find the value of a function at t = ∞.
💡 Hint: Think about what happens to functions at very large time values.
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Challenge Problems
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For the functions f(t) = t^2 and g(t) = e^(-3t), apply the linearity property to compute ℒ{4f(t) - 2g(t)}.
💡 Hint: Look up the transforms for t^2 and e^(-3t).
Given F(s) = 4/(s^2 + 9), utilize both Initial and Final Value Theorems to find the initial and final values without deriving f(t).
💡 Hint: Think about what happens as s approaches these two different infinite situations.
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