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[1]:= $Version Out[1]= 7.0 for Linux x86 (64-bit) (February 18, 2009) In[2]:= f[t_] = Root[1 + t*#1 + #1^6 & , 2]; In[3]:= Plot[f[Exp[t]], {t, Log[6/5^(5/6)], 10}, FrameTicks -> {Transpose[{Range[10], Exp[Range[10]]}], 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[4]:= Limit[f[x], x -> Infinity] Out[4]= -Infinity oops... In[5]:= Limit[f[Exp[x]], x -> Infinity] Out[5]= 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[6]:= << "NumericalCalculus`" Chop[NLimit[f[x], x -> Infinity, Terms -> 11]] Out[7]= 0 as expected. And: In[8]:= NLimit[f[Exp[x]], x -> Infinity] Out[8]= 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