Limit of (n)^(.5)/ln n: A Guide to Finding the Limit of a Sequence

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In summary, the limit of (n)^(.5)/ln n as n approaches infinity is equal to zero. L'Hopital's rule can be used to evaluate this limit, as it is an indeterminate form of type 0/0. Finding the limit helps us understand the behavior of the function as n approaches infinity and can also be used to determine the growth rate of the function. This limit can be applied to any function that has a square root in the numerator and a logarithm in the denominator.
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remaan
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Homework Statement


How to find the limit of :
(n) ^(.5) / ln n


Homework Equations





The Attempt at a Solution



I tied doing it, I got inifity, is that right ?
 
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  • #2
Yes. L'Hopital.
 
  • #3
Uha, and what if I want determine the Convergence or Divergece of it ?

What test to use?

I think, that we should " limit of comparision test"
 
  • #4
The limit comparison test is for series, not sequences.
 

What is the limit of (n)^(.5)/ln n as n approaches infinity?

The limit is equal to zero.

Can the limit of (n)^(.5)/ln n be evaluated using L'Hopital's rule?

Yes, L'Hopital's rule can be used to evaluate this limit.

Is (n)^(.5)/ln n an indeterminate form?

Yes, it is an indeterminate form of type 0/0.

What is the significance of finding the limit of (n)^(.5)/ln n?

Finding the limit helps us understand the behavior of the function as n approaches infinity. It can also be used to determine the growth rate of the function.

Is this limit specific to (n)^(.5)/ln n or does it apply to other functions as well?

This limit can be applied to any function that has a square root in the numerator and a logarithm in the denominator.

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