• Support PF! Buy your school textbooks, materials and every day products Here!

An Implication of a limit rule

  • Thread starter Rayquesto
  • Start date
  • #1
318
0

Homework Statement



If lim (x->∞) [ln(x^(1/x))]=0 and lim (x->∞) x^(1/x)=1, then does this

=>

lim (x->∞) [ln(x^(1/x))]= ln(lim(x->∞) [(x^(1/x))]) = ln(1)??

Homework Equations



lim (x->∞) [ln(x^(1/x))]=0 and lim (x->∞) x^(1/x)=1

The Attempt at a Solution



lim (x->∞) [ln(x^(1/x))]= ln(lim(x->∞) [(x^(1/x))] = ln(1)
 

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,224
947

Homework Statement



If lim (x->∞) [ln(x^(1/x))]=0 and lim (x->∞) x^(1/x)=1, then does this

=>

lim (x->∞) [ln(x^(1/x))]= ln(lim(x->∞) [(x^(1/x))]) = ln(1)??

Homework Equations



lim (x->∞) [ln(x^(1/x))]=0 and lim (x->∞) x^(1/x)=1

The Attempt at a Solution



lim (x->∞) [ln(x^(1/x))]= ln(lim(x->∞) [(x^(1/x))] = ln(1)
Just what is the question?

You do realize that ln(1) = 0, don't you ?
 
  • #3
318
0
Yes, but the question refers to the limit rules. This is what I am asking:


lim (x->∞) [ln(x^(1/x))]= ln(lim(x->∞) [(x^(1/x))]) = ln(1)??

To put it into words: Can the limit as x approaches infinity of [ln(x^(1/x))] be equal to the natural log of the limit as x approaches infinity of [(x^(1/x))] since lim (x->∞) [ln(x^(1/x))]=0 and lim (x->∞) x^(1/x)=1?
 

Related Threads for: An Implication of a limit rule

Replies
3
Views
287
  • Last Post
Replies
6
Views
3K
Replies
1
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
10
Views
604
  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
12
Views
648
Top