# 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 ________________

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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

by (42.1k points)
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  $\frac{b}{(s+1)(s+a)}$

= $\frac{b}{a}$.

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