Limit Question (Using logarithm and L'Hopital's Rule)

[neden]

Homework Statement

http://img213.imageshack.us/img213/4474/scan0001ha.jpg

 

[rochfor1]

Note that ln(a/b) != ln a/ln b

 

[neden]

Oh, right! ln(x/y) = lnx - lny

Ok, edit:

http://img130.imageshack.us/img130/5672/scan0003va.jpg

Something tells me that line 3 is wrong!
Any suggestions on what to do after line 2, I know I need to drop the x exponent on (1+(1/x)) using logarithm

 

[Scigatt]

You're going about it completely the wrong way. Try moving the limit around in the original expression.

 

[neden]

I apologize but what do you mean and how? Can you show some steps it's been a while and due date is coming up soon and I still haven't figured it out!

 

[Scigatt]

I apologize but what do you mean and how? Can you show some steps it's been a while and due date is coming up soon and I still haven't figured it out!

Remember that:

$$e = \lim_{n\to\infty} \left( 1 + \frac{1}{n} \right)^n$$

by definition. Also remember the laws for manipulating limits.