Re: piecewise vs which

• To: mathgroup at smc.vnet.net
• Subject: [mg60112] Re: [mg60101] piecewise vs which
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Sat, 3 Sep 2005 02:06:00 -0400 (EDT)
• References: <200509020833.EAA05912@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```The answer you seek is in the documentation for Piecewise. All
Piecewise functions have a default value of zero on their undefined
intervals. You can change this.

> 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!
>
>
>

--
Chris Chiasson
http://chrischiasson.com/
1 (810) 265-3161

```

• Prev by Date: Re: Trig functions expressed as Radicals
• Next by Date: Re: piecewise vs which
• Previous by thread: piecewise vs which
• Next by thread: Re: piecewise vs which