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

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)   (Show Source): You can put this solution on YOUR website!
Has been addresed
Answer by ikleyn(52776)   (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 = 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 ( ! )

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