The region of convergence (ROC) of x(z) is the set of all values of z for which x(z) attains a finite value.
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They are similar. In many problems, both methods can be used. You can view Fourier transform is the Laplace transform on the circle, that is |z|=1. When you do Fourier transform, you don't need to worry about the convergence region. However, you need to find the convergence region for each Laplace transform. The discrete version of Fourier transform is discrete Fourier transform, and the discrete version of Laplace transform is Z-transform.
It depends on the country (region) whose currency it is because that determines the coinage. For example there is a 20 cent coin in the Euro but not in the US dollar.
Geometric Probability
The slope-intercept inequality is an equation of the form y < mx + c. The inequality can be reversed, and in both cases can be strict or not. In all cases the equality divides the Cartesian plane into two and the inequality determines which side of the straight line is the valid region, and whether or not the line itself should be included.
The inguinal region