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Re: Wrong limit?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104700] Re: [mg104654] Wrong limit?
  • From: "David Park" <djmpark at comcast.net>
  • Date: Sat, 7 Nov 2009 06:48:20 -0500 (EST)
  • References: <5924809.1257503143831.JavaMail.root@n11>

Because in two dimensions a limit may not be well defined and can depend
upon the direction of approach to the limit point. Look at the plot.

Plot3D[(x^2 - a^2)/(5 x^2 - 4 a x - a^2), {x, -1, 1}, {a, -1, 1},
 MaxRecursion -> 6,
 AxesLabel -> {"x", "a", "f"}]

Check a basic calculus book on limits and dependence on direction.


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  



From: wiso [mailto:gtu2003 at alice.it] 

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




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