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