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If X(s), the Laplace transform of signal x(t) is given by \(X\left( s \right) = \frac{{\left( {s + 2} \right)}}{{\left( {s + 1} \right){{\left( {s + 3} \right)}^2}}},\) then the value of x(t) as t → ∞ is _______.

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\(X\left( s \right) = \frac{{\left( {s + 2} \right)}}{{\left( {s + 1} \right){{\left( {s + 3} \right)}^2}}}\) 

Using final value of theorem,

\(\begin{array}{l} \mathop {{\rm{lt}}}\limits_{t \to \infty } x\left( t \right) = \mathop {{\rm{lt}}}\limits_{s \to 0} sX\left( s \right)\\ \mathop {{\rm{lt}}}\limits_{s \to 0} s.\frac{{\left( {s + 2} \right)}}{{\left( {s + 1} \right){{\left( {s + 3} \right)}^2}}} = 0 \end{array}\) 

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