Question

The steady state value of F (t), if it is known that F(s) = \(\frac{b}{s(s+1)(s+a)}\), where a>0, is ________________

(a) \(\frac{b}{a}\)

(b) \(\frac{a}{b}\)

(c) 1

(d) Cannot be determined

I have been asked this question in exam.

My question comes from Region of Convergence in section Laplace Transform and System Design of Signals and Systems

Answer 1

The correct answer is (a) \(\frac{b}{a}\)

The best I can explain: F (∞) = lims→0 s F(s)

= lims→0 \(\frac{sb}{s(s+1)(s+a)}\)

= lims→0  \(\frac{b}{(s+1)(s+a)}\)

= \(\frac{b}{a}\).