Practice Proof Of First Derivative (1.1.4) - Laplace Transform of Derivatives

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6 sample questions

Question 1.
What is the Laplace Transform of f(t) = t?
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Use the basic formula of Laplace Transform.
Question 2.
Write the formula for L{f'(t)}.
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Recall the transformation equation discussed.
3Question 3.
What is the Laplace Transform of f'(t)?
- sF(s) + f(0)
- sF(s) - f(0)
- 0
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Remind yourself of the transformation formulas.
4Question 4.
True or False: The Laplace Transform can only be used for first derivatives.
- True
- False
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Think about the different orders of derivatives we've covered.
Question 5.
Given f(t) = e^{at} sin(bt), find the Laplace Transform using properties of derivatives implicitly.
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Use the formula for the Laplace Transform of functions multiplied by an exponential.
Question 6.
Prove the formula for L{f(n)(t)} = s^nF(s) - Σ from k=0 to n-1 of s^{n-1-k} f^(k)(0).
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Work step-by-step through the integrations as shown in the previous examples.

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