Re: piecewise vs which

*To*: mathgroup at smc.vnet.net*Subject*: [mg60128] Re: piecewise vs which*From*: Helen Read <hpr at together.net>*Date*: Sat, 3 Sep 2005 02:06:27 -0400 (EDT)*References*: <df9437$620$1@smc.vnet.net>*Reply-to*: read at math.uvm.edu*Sender*: owner-wri-mathgroup at wolfram.com

Bradley Stoll wrote: > Consider defining a function in Mathematica (v. 5.2) in two different > ways: f[x_]=Piecewise[{{x^2,x<2},{3x,x>2}}] and > g[x_]=Which[x<2,x^2,x>2,3x]. Notice that 2 is not in the domain of > either function. However, if I ask for f[2], Mathematica returns 0 and if I ask > for g[2] Mathematica (correctly) returns nothing. Is this a bug with > Mathematica (that Mathematica returns 0 for f[2]), since 2 is not in the domain? > While I have eyes, there is another question regarding limits. Is it > the case that Limit[f[x],x->2] defaulted as > Limit[f[x],x->2,Direction->-1] (a right hand limit)? Both return 6 in > the above example. I'm using Mathematica in my calculus class and would > like to explain why Mathematica does certain things. It doesn't seem > that it would've been too difficult to just have two subroutines (a > right and left hand limit) to determine whether a 'full' limit actually > existed. Limit does indeed default to Direction->-1. Try, for example, Limit[Abs[x]/x,x->0] I don't like this at all. For purposes of teaching calculus students, where we are only concerned with real numbers and are not taking limits in the complex plane, I would like Limit to check from both directions. -- Helen Read University of Vermont

**Follow-Ups**:**Re: Re: piecewise vs which***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>