RE: Asymptote mystery...
- To: mathgroup at smc.vnet.net
- Subject: [mg38844] RE: [mg38834] Asymptote mystery...
- From: "Florian Jaccard" <jaccardf at eicn.ch>
- Date: Thu, 16 Jan 2003 03:18:35 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
There is no asymptote in -2, but a "hole" :
In[21]:=
f[x_] := (x + 2)/(Sqrt[x^2] - 2)
In[41]:=
Limit[f[x], x -> -2]
Out[41]=
-1
In[42]:=
Limit[f[x], x -> -2, Direction -> 1]
Out[42]=
-1
In[43]:=
Limit[f[x], x -> -2, Direction -> -1]
Out[43]=
-1
In fact, f(x)=-1 for all x<0 (x!=-2)
If you want to see a good graphic of the function, proceed like this :
In[26]:=
p1 = Plot[f[x], {x, -4, -2.1}, AspectRatio -> Automatic, PlotRange -> {-5,
5},
Epilog -> Circle[{-2, -1}, 0.1], DisplayFunction -> Identity];
In[37]:=
p2 = Plot[f[x], {x, -1.9, 2}, Epilog -> {Dashing[{0.02}], Line[{{2, -5}, {2,
5}}]},
DisplayFunction -> Identity];
In[35]:=
p4 = Graphics[{Dashing[{0.02}], Line[{{2, -5}, {2, 5}}]}];
In[30]:=
p3 = Plot[f[x], {x, 2, 5}, DisplayFunction -> Identity];
In[39]:=
Show[p1, p2, p3, p4, DisplayFunction -> $DisplayFunction];
Meilleures salutations
Florian Jaccard
professeur de Mathématiques
EICN-HES
-----Message d'origine-----
De : Mike Summers [mailto:mike at miscanthus.net]
Envoyé : mer., 15. janvier 2003 08:20
À : mathgroup at smc.vnet.net
Objet : [mg38834] Asymptote mystery...
It seems to me that this:
f[x] = (x + 2)/(Abs[x] - 2)
should show asymptotes at 2 & -2.
Plot[Evaluate[f[x]], {x, -5, 5}] only shows the asymptote at 2.
What am I doing wrong?
Thanks-- Mike