Practice Conditions For Existence (dirichlet Conditions) (1.2) - Laplace Transforms & Applications - Definition of Laplace Transform

Practice: Conditions for Existence (Dirichlet Conditions)

Lesson 1.2Laplace Transforms & Applications - Definition of Laplace Transform

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8 questions

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6 sample questions

Question 1.
What does piecewise continuity mean?
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Think about the continuity of the function.
Question 2.
State the Dirichlet Conditions.
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Consider which two major conditions we discussed.
3Question 3.
What is a requirement for a function to possess a Laplace Transform?
- It must be continuous everywhere
- It must be piecewise continuous
- It can have infinite discontinuities
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Look back at the first condition we discussed.
4Question 4.
True or False: A function growing faster than e^(2t) can be transformed using Laplace.
- True
- False
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Recall the defining rules about growth.
Question 5.
Evaluate if the function f(t) = { 3t for 0 ≤ t < 5; t^2 - 10 for t ≥ 5 } meets the Dirichlet Conditions.
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Analyze the function parts for continuity and check against the nature of growth.
Question 6.
Given f(t) = sin(t) + e^(t^2), determine if it is suitable for Laplace Transform and explain.
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Consider the rapid increase of e^(t^2) compared to its constant multiplicative limits.

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