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GATE 2014 EE (EE1) – Question 14

Signals and Systems · Applications of Fourier Transform for continuous and discrete time signals, Laplace Transform and Z transform · 1 mark · Multiple choice

$X(s)=(3s+5)/(s^2+10s+21)$ is the Laplace transform of x(t). Find x(0⁺).

  1. 0
  2. 3
  3. 5
  4. 21

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Correct answer: (B) 3

Explanation

The initial-value theorem gives x(0+)=lim(s→∞)sX(s), provided there is no impulse at the origin. Here s(3s+5)/(s²+10s+21) tends to3. Therefore **x(0+)=3,B**. The transform is strictly proper and its finite high-frequency limit is consistent with an ordinary initial value.