Practice General Formula (1.1.8) - Laplace Transform of Derivatives - Mathematics - iii (Differential Calculus) - Vol 1

Practice: General Formula

Lesson 1.1.8Laplace Transform of Derivatives

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9 questions

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6 sample questions

Question 1.
What is the Laplace Transform of the function $f(t) = t$ ?
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Use integration by parts to derive.
Question 2.
Calculate $L\{f'''(t)\}$ for $f(t) = e^{3t}$ .
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Remember to apply the formula for the third derivative using initial values.
3Question 3.
What is the formula for the Laplace Transform of the first derivative?
- A) L{f'(t)} = sF(s) + f(0)
- B) L{f'(t)} = sF(s) - f(0)
- C) L{f'(t)} = F(s) - f(0)
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Remember the negative sign for the initial value.
4Question 4.
True or False: The Laplace Transform can convert time-domain functions into frequency-domain functions.
- True
- False
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Consider what the purpose of the Laplace Transform is.
Question 5.
Given the initial value problem defined by the second-order linear homogeneous ODE $y'' - 3y' + 2y = 0$ with initial conditions $y(0) = 1$ and $y'(0) = 0$ , find the general solution using the Laplace Transform.
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Keep track of the initial values and re-arrange the equation.
Question 6.
If $f(t) = t^3 e^{-2t}$ , derive L{f^{(4)}(t)} without computing the individual derivatives.
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Understand how to apply properties and series to achieve this without explicit derivative calculation.

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