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### Limit Evaluation

```
Date: 7/7/96 at 16:21:41
From: Anonymous
Subject: Limit Evaluation

I'm in the first year of electronics in Buenos Aires and I have a
problem with a limit. I have no idea how to begin:

Lim     Root x of (x)
X -> oo

Limit of root X of x, with X -> infinity.
```

```
Date: 7/7/96 at 19:3:28
From: Doctor Anthony
Subject: Re: Limit Evaluation

I believe you are wanting the xth root of x, which is better shown as

x^(1/x)

Let y = x^(1/x)
Now, with a variable as a power, it is usual to take logs.

Take logs (base e) of both sides

ln(y) = (1/x)ln(x)  = ln(x)/x

Now as x -> infinity this becomes inf/inf and we can use l'Hopital's
rule to see what the ratio is becoming as x approaches its limit.

LT(as x->infin.)ln(y) = (diff. of top line)/(diff. of bottom line)
= (1/x)/1
= 1/x
->0 as x -> infin.

If ln(y) -> 0 then y -> 1  and so Lt(as x-> infin.) x^(1/x) = 1

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```

```
Date: 7/7/96 at 20:58:21
From: Anonymous
Subject: Re: Limit Evaluation

Thank you Mr. Anthony, this is the best WWW of math!!
Hernan Gabriel Zapata. (archie@giga.com.ar)
```
Associated Topics:
High School Analysis

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