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}
There is 1 question to complete.

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