RE: Limits: Is there something I'm missing Here?

*To*: mathgroup at smc.vnet.net*Subject*: [mg39345] RE: [mg39333] Limits: Is there something I'm missing Here?*From*: "Florian Jaccard" <jaccardf at eicn.ch>*Date*: Wed, 12 Feb 2003 03:52:01 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hello ! It is true... If you don't specify direction, the direction is automatically chosen as -1(I think), so you can't trust "Limit" without checking the two directions. So in your example, the limit effectively does not exist ! Here a limit function if direction is not specified that is not bad for typically school-type examples : In[14]:= limReal[y_, x_ -> a_] := If[Limit[y, x -> a, Direction -> 1] == Limit[y, x -> a, Direction -> -1] && Im[y /. x -> a + 10^(-6)] == 0 && Im[y /. x -> a - 10^(-6)] == 0, Limit[y, x -> a], "doesn't exist !"] a[x_]:=1/x In[15]:= limReal[a[x], x -> 0] Out[15]= "doesn't exist !" Meilleures salutations Florian Jaccard professeur de Mathématiques EICN-HES -----Message d'origine----- De : Ashraf El Ansary [mailto:Elansary at btopenworld.com] Envoyé : mar., 11. février 2003 10:47 À : mathgroup at smc.vnet.net Objet : [mg39333] Limits: Is there something I'm missing Here? Dear all, One thing I've noticed that if we have a function which has two different limits (given two different directions) at one points , mathematica would be still give an answer though to my understanding the limit doesn't exist in such a case. Consider the following example: a[x_]:=1/x Limit[a[x],x->0,Direction->+1] +Inf Limit[a[x],x->0,Direction->+1] -Inf Limit[a[x],x->0]. +Inf.... Maybe my calculus knowledge is a bit rusty but does the limit exist in this case?? Thank you