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Re: Wrong limit?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104721] Re: Wrong limit?
  • From: Peter Breitfeld <phbrf at t-online.de>
  • Date: Sat, 7 Nov 2009 07:02:14 -0500 (EST)
  • References: <hd0t8u$82a$1@smc.vnet.net>

wiso wrote:

> Look at this:
>
> Limit[(x^2 - a^2)/(5 x^2 - 4 a x - a^2), x -> a]
> Mathematica answer = 1/3
>
> this is ok for a !=0, but if a = 0 the value is 
>
> Limit[(x^2 - a^2)/(5 x^2 - 4 a x - a^2) /. a -> 0, x -> 0]
> 1/5
>

Limit returns a generic result, which is true except for some Values. If
you want to get close tho the "strange" values try to expand your
expression into a series:

Series[(x^2 - a^2)/(5 x^2 - 4 a x - a^2), {x, a, 3}]//Normal

Out= 1/3 - (-a + x)/(9*a) + (5*(-a + x)^2)/(54*a^2) - 
   (25*(-a + x)^3)/(324*a^3)

Now you can easily see, that for a=!0 the limit will be 1/3, but the
case a=0 is special.   

-- 
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de


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