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