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Decide whether or not the Final Value Theorem is applicable to the following functions. If not, indicate why you cannot apply it. If so, apply the Final Value Theorem. Note: you do not need to perform the inverse Laplace transform.a. X(s)= s/3s+7b. X(s)= 10/3s^2+7s+4

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Answer:

a) Yes applicable, x(∞) = 0

b) Yes applicable, x(∞) = 0

Explanation:

Final Value Theroem indicates that final value of x(t) can be found by Laplace Transform X(s) as follows:

[tex]x(\infty)= \lim\limits_{s \to0} sX(s)[/tex]

[tex]a) X(s)= \frac{s}{3s+7}[/tex]

Since the pole is at left side, FVT is applicable

[tex]x(\infty)= \lim\limits_{s \to0} s\frac{s}{3s+7}=0[/tex]

[tex]b) X(s)= \frac{10}{3s^2+7s+4}[/tex]

[tex]\frac{10}{3s^2+7s+4}= \frac{10}{(3s+4 )(s+1)}[/tex]

Since the poles are at left side, FVT is applicable

[tex]x(\infty)= \lim\limits_{s \to0} s \frac{10}{(3s+4 )(s+1)}=0[/tex]

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