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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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