Question

Initial value theorem states that ___________

(a) x(0)=\(\lim_{x\rightarrow ∞} sX(s)\)

(b) x(∞)=\(\lim_{x\rightarrow ∞} sX(s)\)

(c) x(0)=\(\lim_{x\rightarrow 0} sX(s)\)

(d) x(∞)=\(\lim_{x\rightarrow 0} ⁡sX(s)\)

The question was posed to me in exam.

My doubt stems from Laplace Transform by Properties in portion Laplace Transform of Engineering Mathematics

Answer 1

Right answer is (a) x(0)=\(\lim_{x\rightarrow ∞} sX(s)\)

Easiest explanation: Initial value theorem states that

x(0)=\(\lim_{x\rightarrow ∞} sX(s)\)