A limit question

  • Thread starter daniel_i_l
  • Start date
  • #1
daniel_i_l
Gold Member
867
0

Homework Statement


I was doing a problem and got to the following limit:
[tex]lim_{x \rightarrow 0^{+}} x^{\frac{1}{x} - 1}[/tex] I calculated it and got 0 but when I calculated it here:
http://wims.unice.fr/wims/en_tool~analysis~function.en.html
It said that it wans't defined. Am I right?
Thanks.


Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
1,631
4
try the following:
[tex]lim_{x \rightarrow 0^{+}} x^{\frac{1}{x} - 1}=\lim_{x\rightarrow 0^{+}}e^{ln(x)^{\frac{1}{x}-1}}=\lim_{x\rightarrow\ 0^{+}} e^{\frac{1-x}{x}ln(x)}=e^{\lim_{x\rightarrow\ 0^{+}}\frac{1-x}{x} \lim_{x\rightarrow\ 0^{+}}ln(x)}=e^{\infty*(-\infty)}=e^{-\infty}=0[/tex]
 
  • #3
daniel_i_l
Gold Member
867
0
Thanks, that's what I did but the wims calculator confused me.
 

Related Threads on A limit question

  • Last Post
Replies
11
Views
656
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
4
Views
557
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
1
Views
990
  • Last Post
Replies
1
Views
1K
Top