Practice Laplace Transform Of The N-th Derivative (1.1.7)

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6 sample questions

Question 1.
What is the formula for the Laplace Transform of the first derivative?
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Remember the structure involves s and the initial function value.
Question 2.
True or False: The Laplace Transform can only be applied to continuous functions.
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Consider the nature of functions required for transformation.
3Question 3.
What does L{f′(t)} equal?
- sF(s) - f(0)
- sF(s) + f(0)
- F(s) - s
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Think about how derivatives reduce to algebra.
4Question 4.
True or False: The Laplace Transform can be used for integral equations.
- True
- False
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Recall the scope of the transform discussed.
Question 5.
Find the Laplace Transform of f(t) = e^3t cos(4t), using the property L{e^{at} f(t)} = F(s-a).
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Identify a and b from the exponential and cosine components.
Question 6.
Solve the differential equation y'' + 4y = 0 with y(0)=1 and y'(0)=0 using the Laplace Transform.
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Transform each term carefully while applying initial conditions.

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