Re: Re: piecewise vs which

*To*: mathgroup at smc.vnet.net*Subject*: [mg60137] Re: [mg60128] Re: piecewise vs which*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sun, 4 Sep 2005 03:02:00 -0400 (EDT)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

myLimit[expr1_, x_Symbol->expr2_]:= Module[{t}, If[(t=Limit[expr1,x->expr2,Direction->1])== Limit[expr1,x->expr2,Direction->-1], t,"Limit is undefined"]]; myLimit[Abs[x]/x,x->0] Limit is undefined myLimit[Sin[x]/x,x->0] 1 Bob Hanlon > > From: Helen Read <hpr at together.net> To: mathgroup at smc.vnet.net > Date: 2005/09/03 Sat AM 02:06:27 EDT > Subject: [mg60137] [mg60128] Re: piecewise vs which > > 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 > >