Practice Multiplication By Tn (power Of T) (7.1) - Multiplication by tn (Power of t)

Practice: Multiplication by tn (Power of t)

Lesson 7.1Multiplication by tn (Power of t)

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8 questions

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6 sample questions

Question 1.
What is the Laplace Transform of $e^{at}$ ?
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Recall the basic property of Laplace Transforms.
Question 2.
State the multiplication property when multiplying by $tn$ .
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Think about how differentiation affects the transform.
3Question 3.
What does the multiplication by $tn$ property do to a function's Laplace Transform?
- It massifies the function.
- It shifts the function.
- It differentiates the transform \$n\$ times with alternating sign.
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Focus on how multiplication affects differentiation.
4Question 4.
True or False: The function must be continuous everywhere for the multiplication by $tn$ property to hold.
- True
- False
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Remember the conditions for the Laplace Transform.
Question 5.
Prove the general multiplication property for $n=2$ using integration by parts.
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Use the integration by parts technique for differentiation.
Question 6.
Given $f(t) = e^{2t}$ , find $L\{t^3 f(t)\}$ and show all steps.
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Compute \$L\\{e^{2t}\\}\$ first to establish a solid base for your derivatives.

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