piecewise vs which

• To: mathgroup at smc.vnet.net
• Subject: [mg60101] piecewise vs which
• Date: Fri, 2 Sep 2005 04:33:03 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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!