# The Laplace transform function for the output voltage of a network is expressed in the following form:V_0(s) = (12(s+2))/(s(s+1)(s+3)(s+4))

The Laplace transform function for the output voltage of a network is expressed in the following form:
${V}_{0}\left(s\right)=\frac{12\left(s+2\right)}{s\left(s+1\right)\left(s+3\right)\left(s+4\right)}$
​Determine the final value of this voltage. that is,
${\upsilon }_{0}\left(t\right)$ as $t\to \mathrm{\infty }$
a) 6V
b) 2V
c) 12V
d) 4V
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Liyana Mansell
We will use the expression for final value of f(t):
$f\left(\mathrm{\infty }\right)=\underset{s\to o}{lim}sF\left(s\right)$
${\upsilon }_{0}\left(\mathrm{\infty }\right)=\underset{s\to o}{lim}s\left(\frac{12\left(s+2\right)}{s\left(s+1\right)\left(s+3\right)\left(s+4\right)}\right)$
$=\underset{s\to o}{lim}\left(\frac{12\left(s+2\right)}{s\left(s+1\right)\left(s+3\right)\left(s+4\right)}\right)$
$=\frac{\left(12\right)\left(2\right)}{\left(1\right)\left(3\right)\left(4\right)}$
$=2$