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Re: Evaluation of limit

• To: mathgroup at smc.vnet.net
• Subject: [mg115742] Re: Evaluation of limit
• From: Roland Franzius <roland.franzius at uos.de>
• Date: Wed, 19 Jan 2011 05:30:41 -0500 (EST)
• References: <ih3rc9$bfl$1@smc.vnet.net>

Am 18.01.2011 11:51, schrieb Dr. C. S. Jog:
> If I give the command
>
> In[1]:= Limit[Cosh[x]+Sinh[x]^2*Log[Tanh[x/2]],x->Infinity]
>
> I get
>                                   x          2
> Out[1]= Limit[Cosh[x] + Log[Tanh[-]] Sinh[x] , x ->  Infinity]
>                                   2
>
> instead of zero. This result can be verified numerically (of course, by
> using higher precision than the default).

The numerical evaluation is instable, oscillating for x >10 as seen by 
Plot, thanks to the general flaw of Mathematica to handle the algebra of 
Log and ArcTan functions properly.

Replace the hyperbolic functions by

Cosh[x]-> 1/2 (q+1/q), Sinh[x]->1/2(q-1/q), Tanh[x/2]-> (q-1)/(q+1)

and let q->oo.

Since one and a half decade I am waiting for easy to use standard 
commands like

LogExpand, LogTogether, LogAssumptions for Simplify, LogToTrig etc.

-- 

Roland Franzius