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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[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






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