Re: Calculus : limits

• To: mathgroup at smc.vnet.net
• Subject: [mg51310] Re: Calculus : limits
• From: p-valko at tamu.edu (Peter Valko)
• Date: Thu, 14 Oct 2004 06:35:39 -0400 (EDT)
• References: <ckfs34\$isl\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Strictly speaking Direction option has to be specified.
The default is "Automatic" but in this case Mathematica takes (seemingly)
Direction-> -1 as default.
Limit[(Abs[Sin[x]-Sin[2 x]]) / x, x->0,Direction->-1]
Limit[(Abs[Sin[x]-Sin[2 x]]) / x, x->0,Direction->1]
will give you two right answers (that are not equal.)
The truth of the matter is, that Calculus-type functions do not handle
Abs very well and if possible I use other things, e.g. UnitStep.
P.

Amir <z64043 at netscape.net> wrote in message news:<ckfs34\$isl\$1 at smc.vnet.net>...
> 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.
>
> Amir

```

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