Question

The Laplace transorm af a function f(t) is $F\left(s\right)=\frac{5s^2+23s+6}{s(s^2+2s+2)}$. As $t\to \infty ,$ f(t) approaches?

• A. 3
• B. 5
• C. $\frac{17}{2}$
• D. $\alpha$

Answer 1

The correct option is A 3

Using final value theorem
$f\left(\infty \right)={lim}_{s\to 0}\left[sF\right(s\left)\right]={lim}_{s\to 0}\left[\frac{5s^2+23s+6}{s^2+2s+2}\right]=3$