Re: piecewise vs which

• To: mathgroup at smc.vnet.net
• Subject: [mg60117] Re: [mg60101] piecewise vs which
• From: Pratik Desai <pdesai1 at umbc.edu>
• Date: Sat, 3 Sep 2005 02:06:05 -0400 (EDT)
• References: <200509020833.EAA05912@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.
>

If you look at the help on Piecewise it comes with the following disclosure

Piecewise[{{a, a}, ? }, val] uses default value val if none of the a
apply. The default for val is 0.

Hmm......The other problem might be that this may not be a piecewise
continuous function

Limit[f[x],x->2,Direction->-1]
6
Limit[f[x],x->2,Direction->1]
4

Thanks for bringing this to my attention, I have been using piecewise
with impunity in my codes....may be I should look at them again

Pratik

>  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!
>
>
>
>

--
Pratik Desai
UMBC
Department of Mechanical Engineering
Phone: 410 455 8134

```

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