The initial and final value properties are used to find the initial and final values of a waveform corresponding to a given transform. consider the following signals and determine what their transform's initial and final values would say. How do they compare with simply finding the limit at \(t=0\) and \(t \rightarrow \infty\) ?

(a) \(f_{1}(t)=10 e^{-50 t} \cos (200 t) u(t)\)

(b) \(f_{2}(t)=\left[50 e^{-200 t}-200 e^{-500 t}\right] u(t)\)

(c) \(f_{3}(t)=\left[5 e^{-j 10 t}+5 e^{+j 10 t}\right] u(t)\)