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MathGroup Archive 2001

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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
>
>



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