Question

Find x(∞) if X(s) is given by \(\frac{s-2}{s(s+4)}\).

(a) 1

(b) -1

(c) \(\frac{1}{2}\)

(d) –\(\frac{1}{2}\)

This question was addressed to me in quiz.

Origin of the question is Properties of the Laplace Transform topic in portion Laplace Transform and System Design of Signals and Systems

Answer 1

Correct option is (d) –\(\frac{1}{2}\)

Explanation: Given X(s) = \(\frac{s-2}{s(s+4)}\)

Final value, x(∞) = lims→0 sX(s) = lims→0 \(\frac{(s-2)}{s(s+4)} = -\frac{2}{4} = -\frac{1}{2}\).