Practice Proof Of The First Shifting Theorem (1.6) - Topic 3: First Shifting Theorem

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6 sample questions

Question 1.
What is the Laplace Transform of e^(2t)?
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Use the basic exponential Laplace Transform.
Question 2.
What happens to the Laplace Transform when multiplying by e^(at)?
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Refer to the theorem's statement.
3Question 3.
What is the result of applying the First Shifting Theorem if ℒ{f(t)} = F(s)?
- F(s + a)
- F(s - a)
- F(2s)
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Think about how e^(at) affects the Laplace variable.
4Question 4.
True or False: Using the theorem, ℒ{e^(-2t)cos(t)} results in F(s + 2).
- True
- False
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Recall the correct direction of the shift.
Question 5.
Using the First Shifting Theorem, derive the transform for e^(3t)sin(2t).
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First find the transform of sin(2t) then apply the theorem.
Question 6.
Find the Laplace Transform of e^(-5t)(t^3).
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Apply integration by parts, track using the theorem step-by-step.

4 more questions in this section. Enroll free to practise them all.