Practice Definition (12.2) - Inverse Laplace Transform - Mathematics - iii (Differential Calculus)

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6 sample questions

Question 1.
What is L⁻¹{1/s}?
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Consider what function remains constant over time.
Question 2.
What does L⁻¹{1/s²} yield?
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This represents linear growth over time.
3Question 3.
What is the inverse of L{f(t)} = F(s)?
- f(t)
- F(s)
- L⁻¹{F(s)}
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Think about what the operation denotes.
4Question 4.
True or False: The Inverse Laplace Transform only works for polynomial F(s).
- True
- False
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Remember other function types learned in class.
Question 5.
Find L⁻¹{(s + 2)/(s² + 3s + 2)}. Demonstrate utilizing partial fractions.
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Start with the quadratic denominator.
Question 6.
Apply the Convolution Theorem for two functions: f(t)=t and g(t)=e^(-2t). What is the resulting function?
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Utilize the convolution integral format and integrate accordingly.

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