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n^(1/n)
Limit of the function/ n^(1/n)

Limit of the function n^(1/n)

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The solution

You have entered [src] 
     n ___
 lim \/ n 
n->oo
lim⁡n→∞n1n\lim_{n \to \infty} n^{\frac{1}{n}} 
Limit(n^(1/n), n, oo, dir='-')
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
02468-8-6-4-2-101002
Plot the graph
Rapid solution [src] 
1
11
Expand and simplify
Other limits n→0, -oo, +oo, 1
lim⁡n→∞n1n=1\lim_{n \to \infty} n^{\frac{1}{n}} = 1
lim⁡n→0−n1n=∞\lim_{n \to 0^-} n^{\frac{1}{n}} = \infty
More at n→0 from the left
lim⁡n→0+n1n=0\lim_{n \to 0^+} n^{\frac{1}{n}} = 0
More at n→0 from the right
lim⁡n→1−n1n=1\lim_{n \to 1^-} n^{\frac{1}{n}} = 1
More at n→1 from the left
lim⁡n→1+n1n=1\lim_{n \to 1^+} n^{\frac{1}{n}} = 1
More at n→1 from the right
lim⁡n→−∞n1n=1\lim_{n \to -\infty} n^{\frac{1}{n}} = 1
More at n→-oo
The graph
Limit of the function n^(1/n)
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