What is the set of all values of z for which X(z) attains a finite value?. Single choice.
(1 Point)
a) Radius of convergence
b) Radius of divergence
c) Feasible solution
d) None of the mentioned
Answers
Answer:
b) Radius of divergence
hope it helps you...!
Answer:
The set of all values of z where X(z) converges to a finite value is called as Radius of Convergence(ROC).
Step-by-step explanation:
Radius of convergence
ROC is ∣z∣>∣0. 8j∣=0. 8, i.e. outside the circle of radius 0.8. ROC is determined by the sequence 1+z−3+z−6+...which converges when ∣z−3∣<1 or ∣z∣>1
The diameter of the biggest disc at the series' convergence point is known as the radius of convergence of a power series in mathematics. Either a positive real number or "display style nifty nifty" applies. When it is positive, the power series converges to the Taylor series of the analytical function absolutely and evenly on compact sets inside the open disc with a radius equal to the radius of convergence. The radius of convergence is the shortest or smallest of all the corresponding distances, which are all non-negative integers, measured from the center of the function in the situation of numerous singularities (discontinuities are those numbers of the parameter for which the function is not specified). The radius of convergence is the shortest or smallest of all the estimated distances between the center of the convergence disc and each of the function's singularities, all of which are non-negative values.
determined is the radius of convergence
Half of the interval of convergence's length corresponds to the radius of convergence. The open interval: (a R, a + R) will be included in the interval of convergence if the radius of convergence is R. You apply the Ratio Test to determine R, the radius of convergence.