Re: piecewise vs which

*To*: mathgroup at smc.vnet.net*Subject*: [mg60118] Re: [mg60101] piecewise vs which*From*: Curtis Osterhoudt <gardyloo at mail.wsu.edu>*Date*: Sat, 3 Sep 2005 02:06:06 -0400 (EDT)*References*: <200509020833.EAA05912@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, Bradley, Some similar questions -- but with limits of +/- Infinity -- have been bantered about on this group recently regarding limits. The Piecewise function returns 0 as a default value when a domain isn't given for an argument. I found this from the command ?Piecewise, but it's also in the fuller Help Index documentation, of course. If you make a larger "gap", say, f[x_] := Piecewise[{{x^2, x < 2}, {3*x, x > 10}}] then Piecewise will return 0 for values for 2<= x <= 10. For the students' sake you might define f to return Null at "unspecified" arguments, with f[x_] := Piecewise[{{x^2, x < 2}, {3*x, x > 10}}, Null] This should plot and behave more as you expect. Also, the Limit function now works as you'd expect, including directed limits: try Limit[f[x], x -> 2, Direction -> 1] vs. Limit[f[x], x -> 2]. Regards, Curtis O. 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. >Thanks! > >Bradley > > > > -- PGP Key ID: 0x235FDED1 Please avoid sending me Word or PowerPoint attachments. http://www.gnu.org/philosophy/no-word-attachments.html

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