Multiple choice

If F (s) = L [f (t)] = $\frac{2(s+1)}{s^2 + 4s + 7}$ then the initial and final values of f(t) are respectively

  1. 0,2

  2. 2,0

  3. 0,2/7

  4. 2/7,0
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using Initial Value Theorem: f(0⁺) = lim_{s→∞} sF(s) = lim s×2(s+1)/(s²+4s+7) = lim 2s²/(s²) = 2. Using Final Value Theorem: f(∞) = lim_{s→0} sF(s) = lim s×2(s+1)/(s²+4s+7) = 2(0)/7 = 0. Initial value is 2, final value is 0.

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