Limit question

  • Thread starter talolard
  • Start date
  • #1
talolard
125
0

Homework Statement


I've done thsi limit, i think I'm half right. I'm sure I have done something wrong, but I'm not sure what.

[tex] lim_{x-> \infty} ( \frac {x+lnx}{x-lnx})^(x/lnx) [/tex]


The Attempt at a Solution


[tex] lim_{x-> \infty} ( \frac {x+lnx}{x-lnx})^{x/lnx} = lim_{x-> \infty} ( \frac {x(1 +\frac {lnx}{x})}{x(1- \frac {lnx}{x})})^{x/lnx}= [/tex]
[tex]
t= \frac {x}{lnx}; lim_{t-> \infty} (\frac {1 + \frac {1}{t}} {1 - \frac{1}{t}})^t= [/tex]
[tex] \frac {e}{e^{-1}}=e^2 [/tex]
 
Last edited:

Answers and Replies

  • #2
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
15,759
2,396
That's right.
 

Suggested for: Limit question

  • Last Post
Replies
1
Views
324
  • Last Post
Replies
5
Views
425
Replies
9
Views
625
  • Last Post
Replies
20
Views
623
  • Last Post
Replies
1
Views
323
  • Last Post
Replies
9
Views
490
Replies
4
Views
690
  • Last Post
Replies
2
Views
365
  • Last Post
Replies
15
Views
675
Replies
3
Views
341
Top