Practice Initial Value Theorem (14.1) - Initial Value Theorem - Mathematics - iii (Differential Calculus)

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6 sample questions

Question 1.
What is the initial value of f(t) if F(s) = 3/(s + 1)?
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Evaluate lim (s→∞)[3s/(s + 1)].
Question 2.
List one condition for applying the Initial Value Theorem.
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Think about the requirements needed for the theorem.
3Question 3.
What does the Initial Value Theorem state about f(t) and F(s)?
- a) lim(t→0+) f(t) = 0
- b) lim(t→0+) f(t) = lim(s→∞) sF(s)
- c) lim(s→0) F(s) = f(0)
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Focus on the relationship between limits involving f(t) and F(s).
4Question 4.
True or False: The Initial Value Theorem can be used with functions that contain impulse functions.
- True
- False
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What happens to the function's continuity?
Question 5.
Apply the Initial Value Theorem to find the initial value of f(t) for F(s) = 6/(s^2 + 3s + 2).
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Simplify the expression before taking the limit.
Question 6.
Determine why the IVT fails for F(s) = e^(-s)/(s + 1) in computing f(0).
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Evaluate the limits carefully.

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