Limits with square roots

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My book is showing this as an intuitive step, but I'm not quite seeing the reasoning behind it.

n**(c/n) → 1 as n → ∞, for, I think, any positive c. But why?
 

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Dick
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My book is showing this as an intuitive step, but I'm not quite seeing the reasoning behind it.

n**(c/n) → 1 as n → ∞, for, I think, any positive c. But why?
Take the log and look at the limit of that. Use l'Hopital's rule, if it doesn't seem intuitive.
 
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  • #3
164
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Take the log and look at the limit of that. Use l'Hopital's rule, if it doesn't seem intuitive.
Thank you very much. I was looking for things to cancel out, since it was written as if it was a basic arithmetic step, and kept backing into the same wall.
 

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