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)
• 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
>
> > 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
> > 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.
>
> --