Re: piecewise vs which

• To: mathgroup at smc.vnet.net
• Subject: [mg60128] Re: piecewise vs which
• From: Helen Read <hpr at together.net>
• Date: Sat, 3 Sep 2005 02:06:27 -0400 (EDT)
• References: <df9437\$620\$1@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.  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.

--
University of Vermont

```

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