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Re: Limits

• To: mathgroup at smc.vnet.net
• Subject: [mg7783] Re: [mg7741] Limits
• From: "Keith S. Mersman" <c621746 at everest.cclabs.missouri.edu>
• Date: Tue, 8 Jul 1997 22:41:01 -0400
• Sender: owner-wri-mathgroup at wolfram.com

Hans, 

The "problem" is that Mathematica does not know if your variables are
positive.  If you take the limit of the numerator, you get 3*(-sk^2*Us^2 + 
Sqrt[sk^4*Us^4]) which is 0 if sk and Us are both positive.  However, for
all applications, this might not be 0.  You can alleviate this problem by
using the ComplexExpand command on your expression.  




On Mon, 7 Jul 1997, Hans Steffani wrote:

> Does Limit[] not know about L'Hospital?
> 
> In[1]= (2 Mi OmegaSyn Rr-3 sk^2 Us^2+
>    Sqrt[-4 Mi^2 OmegaSyn^2 Rr^2 sk^2+9 sk^4 Us^4])/(2 Mi Rr)
> Out[1]=
>                         2   2
> (2 Mi OmegaSyn Rr - 3 sk  Us  + 
>               2         2   2   2       4   4
>     Sqrt[-4 Mi  OmegaSyn  Rr  sk  + 9 sk  Us ]) / (2 Mi Rr)
> 
> In[2]= Limit[%, Mi->0]
> Out[2]=
>                2   2            4   4
> Infinity (-3 sk  Us  + 3 Sqrt[sk  Us ])
> ---------------------------------------
>                   Rr
> 
> In[3]= Limit[ D[Numerator[%%], Mi]/ D[Denominator[%%], Mi]
>       ,Mi->0 ] (* Is L'Hospital possible? *)
> Out[3]= OmegaSyn
> 
> Hans Friedrich Steffani
> --
> Hans Friedrich Steffani
> Institut fuer Elektrische Maschinen und Antriebe, TU Chemnitz-Zwickau
> mailto:hans.steffani at e-technik.tu-chemnitz.de
> http://www.tu-chemnitz.de/~hfst/
> 
>