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RE: Limits: Is there something I'm missing Here?
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:= 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:= limReal[a[x], x -> 0] Out= "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