# Transform Theory

 Question 1
Let $X(s)=\frac{3s+5}{s^{2}+10s+21}$ be the Laplace Transform of a signal x(t). Then, x($0^+$) is
 A 0 B 3 C 5 D 21
GATE EE 2014-SET-1   Signals and Systems
Question 1 Explanation:
Given, $X(s)=\left [ \frac{3s+5}{s^2+10s+21} \right ]$
Using initial value theorem,
\begin{aligned} x(0^+) &= \lim_{s \to \infty }[sX(s)]\\ x(0^+) &= \lim_{s \to \infty } \left [ \frac{s(3s+5)}{s^2+10+21} \right ] \\ &= \lim_{s \to \infty }\left [ \frac{3+\frac{5}{s}}{1+\frac{10}{s}+\frac{21}{s^2}} \right ]=3 \end{aligned}
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