       there is an "oops" with Root and Limit

• To: mathgroup at smc.vnet.net
• Subject: [mg108992] there is an "oops" with Root and Limit
• From: Peter Pein <petsie at dordos.net>
• Date: Fri, 9 Apr 2010 03:33:31 -0400 (EDT)

```Dear group,

please have a look at the following!

In:= \$Version
Out= 7.0 for Linux x86 (64-bit) (February 18, 2009)
In:= f[t_] = Root[1 + t*#1 + #1^6 & , 2];
In:= Plot[f[Exp[t]], {t, Log[6/5^(5/6)], 10},
FrameTicks -> {Transpose[{Range, Exp[Range]}], None, None,
-(Range[0, 15]/20.)}, Axes -> None, Frame -> True, PlotRange -> All]

this shows that f tends to 0 as x goes to infinity and I can't imagine
why "something strange" should happen for x>E^10.

In:= Limit[f[x], x -> Infinity]
Out= -Infinity

oops...

In:= Limit[f[Exp[x]], x -> Infinity]
Out= Limit[Root[1 + E^x*#1 + #1^6 & , 2], x -> Infinity]

...well, I could not guess this result ;-)
Option "Assumptions->Element[x,Reals] leads to no change.

In:= << "NumericalCalculus`"
Chop[NLimit[f[x], x -> Infinity, Terms -> 11]]
Out= 0

as expected. And:

In:= NLimit[f[Exp[x]], x -> Infinity]
Out= 0.

similarly.

Finally, N[f[10^1234]] gives -1*10^(-1234) which can be called a
"negative zero with a huge value (for a zero)".

So the question arises:

WTH happens inside "Limit" when handling Root-objects?

Thanks,
Peter

```

• Prev by Date: Using numbers close to to zero in Mathematica version 6
• Next by Date: Re: if using Mathematica to solve an algebraic problem
• Previous by thread: Re: Using numbers close to to zero in Mathematica version 6
• Next by thread: Re: ParametricPlot3D - plane appears contracted in some directions