Help with Determining the Limit of the Sequence Quesiton

[student93]

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.

 

[Dick]

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.