Re: Different limits for simplied and non-simplified function
- To: mathgroup at smc.vnet.net
- Subject: [mg45052] Re: Different limits for simplied and non-simplified function
- From: drbob at bigfoot.com (Bobby R. Treat)
- Date: Sun, 14 Dec 2003 06:22:55 -0500 (EST)
- References: <br4238$j12$1@smc.vnet.net> <br9hr8$d0t$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
The inner limit doesn't exist for n close to 0, so Mathematica
shouldn't give a limit. Once it's giving you a bogus limit at all, it
isn't surprising if it gives different answers for r and R.
For -0.5<n<0, r is real for v<0 but Im[r] tends to +Infinity for v>0.
For 0<n<0.5, just the opposite.
As for the real part, for n nonzero (between -1 and 1), the limit from
the right is Infinity while the limit from the left is -Infinity.
To see all this, look at plots like this one, with various
combinations of Re[r], Im[r], n->(negative numbers, positive numbers),
and see all the combinations that arise. The inner limit clearly
doesn't exist, so the outer limit can't even get off the ground.
Plot[Evaluate[{Re[r]} /. n -> .1], {v, -.000001, .000001},
PlotStyle -> {Blue}]
Bobby
"Mukhtar Bekkali" <mbekkali at hotmail.com> wrote in message news:<br9hr8$d0t$1 at smc.vnet.net>...
> I think I specified h wrongly. The correct function should be
> h=1+(n*v)^(n+2). r and R are the same as before. Then limits are
> different.
>
>
> "Mukhtar Bekkali" <mbekkali at hotmail.com> wrote in message
> news:br4238$j12$1 at smc.vnet.net...
> > I have a function h=1+(n*v)^n-2. Define r=h/D[h,v] and R=Simplify[r].
> Then
> > Limit[Limit[r,v->0],n->0]=infinity, while Limit[Limit[R,v->0],n->0]=0.
> How
> > is this possible, ain't r and R the same thing?
> >
> >
> >