8. Initial and Final Value Theorems

  • Initial Value Theorem \[\lim_{t\rightarrow 0}f(t)= \lim_{s\rightarrow \infty} [sF(s)]\] It helps to determine the value of the time function \(f(t)\) at \(t=0\) without finding the inverse of \(F(s)\).

  • Final Value Theorem \[\lim_{t\rightarrow \infty}f(t) = \lim_{s\rightarrow 0} [sF(s)]\] It helps to determine the steady-state value of the system response.