Re: piecewise vs which

*To*: mathgroup at smc.vnet.net*Subject*: [mg60129] Re: piecewise vs which*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Sun, 4 Sep 2005 03:01:52 -0400 (EDT)*Organization*: The Open University, Milton Keynes, U.K.*References*: <200509020833.EAA05912@smc.vnet.net> <dfbf3g$io7$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Curtis Osterhoudt wrote: > Hi, Bradley, > > Some similar questions -- but with limits of +/- Infinity -- have > been bantered about on this group recently regarding limits. > > The Piecewise function returns 0 as a default value when a domain > isn't given for an argument. I found this from the command ?Piecewise, > but it's also in the fuller Help Index documentation, of course. If you > make a larger "gap", say, > > f[x_] := Piecewise[{{x^2, x < 2}, {3*x, x > 10}}] > > > then Piecewise will return 0 for values for 2<= x <= 10. > > For the students' sake you might define f to return Null at > "unspecified" arguments, with > > f[x_] := Piecewise[{{x^2, x < 2}, {3*x, x > 10}}, Null] > > > This should plot and behave more as you expect. Also, the Limit function > now works as you'd expect, including directed limits: try > > Limit[f[x], x -> 2, Direction -> 1] > > vs. > > Limit[f[x], x -> 2]. > Hi Curtis, I might have miss something but the issue about the limit does not seem to be solved if the function is only discontinuous at one point, say 2 as in the original question, rather than not being defined over an interval. Compare In[1]:= Clear[f] f[x_] := Piecewise[{{x^2, x < 2}, {3*x, x > 10}}, Null] Limit[f[x], x -> 2, Direction -> 1] Limit[f[x], x -> 2, Direction -> -1] Limit[f[x], x -> 2] Out[3]= 4 versus In[6]:= Clear[f] f[x_] := Piecewise[{{x^2, x < 2}, {3*x, x > 2}}, Null] Limit[f[x], x -> 2, Direction -> 1] Limit[f[x], x -> 2, Direction -> -1] Limit[f[x], x -> 2] Out[8]= 4 Out[9]= 6 Out[10]= 6 In[11]:= $Version Out[11]= "5.2 for Microsoft Windows (June 20, 2005)" I believe, although I may be wrong, that the limit can be handled correctly only by defining your own limit function (see for example David Park's message in this thread). Best regards, /J.M.

**References**:**piecewise vs which***From:*"Bradley Stoll" <BradleyS@harker.org>