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MathGroup Archive 2004

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Re: Calculus : limits

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51330] Re: Calculus : limits
  • From: astanoff_otez_ceci at yahoo.fr (astanoff)
  • Date: Thu, 14 Oct 2004 06:37:18 -0400 (EDT)
  • Organization: Gyptis.org les Linuxiens normaux
  • References: <ckfs34$isl$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Amir wrote:
> Hi,
> I'd like to find the limit of
> Limit[(Abs[Sin[x]-Sin[2 x]]) / x, x->0]
> I use Mathematica v.5. I get the wrong (??) answer : 1
> While I try to display the graph of this function by using "Plot", it 
> seems that there is no limit at the point x=0.
> Please help...
> Amir
--
If a function is not continuous - which is the case here - you have to use 
the Direction option :

In[1]:=Limit[Abs[Sin[x] - Sin[2x]]/x, x -> 0, Direction -> -1]
Out[1]=1

In[2]:=Limit[Abs[Sin[x] - Sin[2x]]/x, x -> 0, Direction -> 1]
Out[2]=-1

v.a.
--
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