Help with Determining the Limit of the Sequence Quesiton

  • Thread starter student93
  • Start date
  • #1
85
0

Homework Statement



Problem is attached in this post

Homework Equations



Problem is attached in this post


The Attempt at a Solution



Lim n(2^(1/n)-1) as n -> ∞

Lim (2^(1/n)-1)/(1/n) as n -> ∞ -> 0/0 -> Indeterminate Form -> L'Hopital's Rule

However, I can't seem to figure out how to get the derivative of the numerator.
 

Attachments

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,260
619

Homework Statement



Problem is attached in this post

Homework Equations



Problem is attached in this post


The Attempt at a Solution



Lim n(2^(1/n)-1) as n -> ∞

Lim (2^(1/n)-1)/(1/n) as n -> ∞ -> 0/0 -> Indeterminate Form -> L'Hopital's Rule

However, I can't seem to figure out how to get the derivative of the numerator.
Write 2^(1/n) as e^(log(2)/n). Now use the chain rule to find the derivative.
 

Related Threads on Help with Determining the Limit of the Sequence Quesiton

  • Last Post
Replies
4
Views
6K
Replies
14
Views
2K
Replies
5
Views
2K
Replies
3
Views
1K
  • Last Post
Replies
2
Views
705
Replies
2
Views
1K
  • Last Post
Replies
2
Views
587
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
5
Views
4K
Top