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Re: Limit[Sqrt[a^2-2 x c]/x,x->0] fails

  • To: mathgroup at smc.vnet.net
  • Subject: [mg17529] Re: [mg17447] Limit[Sqrt[a^2-2 x c]/x,x->0] fails
  • From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
  • Date: Fri, 14 May 1999 01:13:05 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

 Mathematica finds it difficult to manage cases like this for it necessary
to assume  that a is positve, which is difficult to persuade it to do. It is
much easier in such cases to use infinite series  (provided you know what
you are doing!). In your case the following method gives the right answer:
In[8]:=
Normal[(Sqrt[a^2-2x*c]-a)/x+O[x]^2//PowerExpand]/.x->0
Out[8]=
  c
-(-)
  a


--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp


----------
>From: "Neal E. Tornberg" <neal.e.tornberg at boeing.com>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>Subject: [mg17529] [mg17447] Limit[Sqrt[a^2-2 x c]/x,x->0] fails
>Date: Sun, May 9, 1999, 5:43 PM
>

> If I remember elementary calculus, the limit is -c/a
> The internal Limit gives DirectedInfinity[-a + Sqrt[a^2]) (formatting
> excised)
> After <<Calculus`Limit` I get
>  On::"none": "Message \!\(Power :: \"infy\"\) not found."
> On::"none": "Message \!\(Power :: \"indet\"\) not found."
> On::"none": "Message \!\(\\[Infinity] :: \"indet\"\) not found."
> General::"stop":
>     "Further output of \!\(On :: \"none\"\) will be suppressed during
> this \
> calculation."
>
> For Limit[Sqrt[(25 + 2 x 3] - 5)/x, x -> 0] they both give 3/5 so at
> least THAT works.
>
> HELP! Please. How do I get this to work so I can address more general
> cases where the solution isn't so obvious?
> --
> Neal E. Tornberg
> neal.e.tornberg at boeing.com
>
> Nobody here thinks I speak for Boeing.
> You shouldn't either.
> 


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