How Does the Limit Equal sqrt(e)?

[Guidenable]

Homework Statement

Show that:

Lim [1+1/(2x)]^x = sqrt(e)
x->-inf

2. Homework Equations /theorums

l'hospital's rule

The Attempt at a Solution

Let y= [1+1/(2x)]^x

lny=ln [1+1/(2x)]^x

lny= x ln [1+1/(2x)]

Then
Ln Lim (y)=
x->-inf

Lim (lny)=
x->-inf

Lim x ln [1+1/(2x)]=
x->-inf

By l'hopital

and evaluating the resulting limit as x->-inf

I get 1/2.How does this limit equal the sqrt of "e"?
I know that it does, as i found a limit calculator online and sqrt(e) was the answer... but no matter how I try to do it, I can't get to sqrt"e".

 

[Dick]

You found lim ln(y) is 1/2. What does that make lim y?

 

[Guidenable]

Oh...e^(1/2). Thank you very much! Although i feel a little dumb, the darn thing was staring me in the face. By the way thanks for the quick reply as well.