Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2003
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2003

[Date Index] [Thread Index] [Author Index]

Search the Archive

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






  • Prev by Date: Re: Getting rid of the symbol -> after finding the root
  • Next by Date: RE: Re: Getting rid of the symbol -> after finding the root
  • Previous by thread: Re: Limits: Is there something I'm missing Here?
  • Next by thread: Re: RE: Limits: Is there something I'm missing Here?