Re: Limit question

*To*: mathgroup at smc.vnet.net*Subject*: [mg31500] Re: [mg31441] Limit question*From*: Otto Linsuain <linsuain at andrew.cmu.edu>*Date*: Thu, 8 Nov 2001 04:54:54 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

I have tried substituting x -> 1/x and specifying the Direction: In[1]:= Limit[Exp[1/x]*(x^2),x\[Rule]0,Direction\[Rule]-1] Limit[Exp[x]/(x^2),x\[Rule]Infinity,Direction\[Rule]1] Out[1]= \[Infinity] Out[2]= \!\(\* RowBox[{"Limit", "[", RowBox[{\(\[ExponentialE]\^x\/x\^2\), ",", RowBox[{"x", "\[Rule]", InterpretationBox["\[Infinity]", DirectedInfinity[ 1]]}], ",", \(Direction \[Rule] 1\)}], "]"}]\) " Where Out[2] is just the unevaluated expression. Amazingly, from the other Direction it works! In[3]:= Limit[Exp[1/x]*(x^2),x\[Rule]0,Direction\[Rule]1] Limit[Exp[x]/(x^2),x\[Rule]-Infinity,Direction\[Rule]-1] Out[3]= 0 Out[4]= 0 This is also quite meaningless, since you don't approach Infinity from direction -1 or -Infinity from direction +1 In[5]:= Limit[Exp[x]/(x^2),x\[Rule]Infinity,Direction\[Rule]-1] Limit[Exp[x]/(x^2),x\[Rule]-Infinity,Direction\[Rule]1] Out[5]= 0 Out[6]= \!\(\* RowBox[{"Limit", "[", RowBox[{\(\[ExponentialE]\^x\/x\^2\), ",", RowBox[{"x", "\[Rule]", InterpretationBox[\(-\[Infinity]\), DirectedInfinity[ -1]]}], ",", \(Direction \[Rule] 1\)}], "]"}]\) Out[6] is again unevaluated. But the results obtained using Exp[1/x] x^2 as x->0 are right. The ones obtained using Exp[x]/x^2 as x-> Infinity are the ones that are worng, most of the time. Otto Linsuain. On Wed, 7 Nov 2001, Leonard Howell wrote: > I'm trying to evaluate Limit [Exp[x] * (1/x^2), x-> Infinity] with > Mathematica but can not seem to get the correct answer of Infinity. Next, I > want Limit [Exp[x] /( x!), x-> Infinity] but can't get it either. Can > someone please provide guidance? > > Thanks, Leonard > >