Fr.: fonction continue
The function y = f(x) is called continuous at the point x = x0 if it is defined in some neighborhood of the point x0 and if lim Δy = 0 when Δx → 0.
piecewise continuous function
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Fr.: fonction continue par morceaux
A function f(x) in an interval if :1) the interval can be divided into a finite number of pieces in each of which f(x) is continuous, and 2) the limits of f(x) as x approaches the boundary point of each piece are finite. In other words, a piecewise continuous function is one that is made up of a finite number of continuous pieces.