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Re: Calculus : limits

• To: mathgroup at smc.vnet.net
• Subject: [mg51338] Re: Calculus : limits
• From: "Peltio" <peltio at twilight.zone>
• Date: Thu, 14 Oct 2004 06:37:54 -0400 (EDT)
• References: <ckfs34$isl$1@smc.vnet.net>
• Reply-to: "Peltio" <peltioNOSP at Mdespammed.com.invalid>
• Sender: owner-wri-mathgroup at wolfram.com

"Amir"

>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.

Yep, the limit from the left is -1, while that from the right is +1.
They can hardly agree in zero. : ]
Ultimately your limit is equivalent to that of Abs[x]/x for x->0
You should load the package Calculus`Limit` to compute limits with
discontinuos functions such as Abs.
(But don't forget, as you've just done, to double check the result you get).

cheers,
Peltio
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