piecewise vs which

*To*: mathgroup at smc.vnet.net*Subject*: [mg60101] piecewise vs which*From*: "Bradley Stoll" <BradleyS at harker.org>*Date*: Fri, 2 Sep 2005 04:33:03 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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. Thanks! Bradley

**Follow-Ups**:**Re: piecewise vs which***From:*Curtis Osterhoudt <gardyloo@mail.wsu.edu>

**Re: piecewise vs which***From:*Pratik Desai <pdesai1@umbc.edu>

**Re: piecewise vs which***From:*Chris Chiasson <chris.chiasson@gmail.com>