SOLUTION: without L'Hospitals rule prove that : limt(x^(1/x)) = 1 when (x → ∞)

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Question 1197595: without L'Hospitals rule prove that :
limt(x^(1/x)) = 1 when (x → ∞)
Found 2 solutions by ewatrrr, ikleyn:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Has been addresed

Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.

(1)   I am glad to see that after my notice you posted a fixed version.

       This time, it is in correct mathematical form, so I will help you.


(2)   If you take logarithm of both sides of your equation,  you will see that your statement is equivalent to this one

       lim ln%28x%29%2Fx = 0   as x --> infinity.


(3)   This last statement is proven under this link

       https://www.youtube.com/watch?v=QCAax866If4

       (youtube video-lesson)  without using the  L'Hospital rule.


Have fun  ( ! )