# Smoothness

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 July 30, 2001, 04:52 Smoothness #1 zhor Guest   Posts: n/a Hi, Function y = |x| belongs to the class C^0, but does not belong to C^1. And what function belongs to C^1, but does not belong to C^2?

 July 30, 2001, 06:41 Re: Smoothness #2 John C. Chien Guest   Posts: n/a (1). given two curves, jointed at at point, then the smoothness is C^0. Zeroth order continuous, I guess. (2). if you can also find the first order derivative at that point, single-valued, then you have C^1. That is, both the function and its derivative are continuous. (3). So, function x will be continuous, and also has continuous first derivative, and is belong to C^1. (1st derivative is Continuous.)

 July 30, 2001, 12:00 Re: Smoothness #3 sylvain Guest   Posts: n/a f(x) = abs(x) is C^0 over [-2,+2] because f'(x) = -1 over [-2,0[ f'(x) = +1 over ]0,+2] and it's undefined at 0. F(x) = int from{-2} to{x} of (abs(t)) dt = x*abs(x)/2 + 2 is C^1 since its first derivative is abs(x) wich is C^0.

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