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

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

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You have entered [src] 
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 lim x /  - 
x->oo\/   x
lim⁡x→∞(1x)1x\lim_{x \to \infty} \left(\frac{1}{x}\right)^{\frac{1}{x}} 
Limit((1/x)^(1/x), x, 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
02468-8-6-4-2-1010010000000000
Plot the graph
Rapid solution [src] 
1
11
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(1x)1x=1\lim_{x \to \infty} \left(\frac{1}{x}\right)^{\frac{1}{x}} = 1
lim⁡x→0−(1x)1x=∞\lim_{x \to 0^-} \left(\frac{1}{x}\right)^{\frac{1}{x}} = \infty
More at x→0 from the left
lim⁡x→0+(1x)1x=∞\lim_{x \to 0^+} \left(\frac{1}{x}\right)^{\frac{1}{x}} = \infty
More at x→0 from the right
lim⁡x→1−(1x)1x=1\lim_{x \to 1^-} \left(\frac{1}{x}\right)^{\frac{1}{x}} = 1
More at x→1 from the left
lim⁡x→1+(1x)1x=1\lim_{x \to 1^+} \left(\frac{1}{x}\right)^{\frac{1}{x}} = 1
More at x→1 from the right
lim⁡x→−∞(1x)1x=1\lim_{x \to -\infty} \left(\frac{1}{x}\right)^{\frac{1}{x}} = 1
More at x→-oo
The graph
Limit of the function (1/x)^(1/x)
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