Re: piecewise vs which

*To*: mathgroup at smc.vnet.net*Subject*: [mg60117] Re: [mg60101] piecewise vs which*From*: Pratik Desai <pdesai1 at umbc.edu>*Date*: Sat, 3 Sep 2005 02:06:05 -0400 (EDT)*References*: <200509020833.EAA05912@smc.vnet.net>*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. > If you look at the help on Piecewise it comes with the following disclosure Piecewise[{{a, a}, ? }, val] uses default value val if none of the a apply. The default for val is 0. Hmm......The other problem might be that this may not be a piecewise continuous function Limit[f[x],x->2,Direction->-1] 6 Limit[f[x],x->2,Direction->1] 4 Thanks for bringing this to my attention, I have been using piecewise with impunity in my codes....may be I should look at them again Pratik > 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 > > > -- Pratik Desai Graduate Student UMBC Department of Mechanical Engineering Phone: 410 455 8134

**References**:**piecewise vs which***From:*"Bradley Stoll" <BradleyS@harker.org>