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Limit of the function/ x^x

Limit of the function x^x

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The solution

You have entered [src] 
      x
 lim x 
x->oo
lim⁡x→∞xx\lim_{x \to \infty} x^{x} 
Limit(x^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
02468-8-6-4-2-1010020000000000
Plot the graph
Rapid solution [src] 
oo
∞\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞xx=∞\lim_{x \to \infty} x^{x} = \infty
lim⁡x→0−xx=1\lim_{x \to 0^-} x^{x} = 1
More at x→0 from the left
lim⁡x→0+xx=1\lim_{x \to 0^+} x^{x} = 1
More at x→0 from the right
lim⁡x→1−xx=1\lim_{x \to 1^-} x^{x} = 1
More at x→1 from the left
lim⁡x→1+xx=1\lim_{x \to 1^+} x^{x} = 1
More at x→1 from the right
lim⁡x→−∞xx=∞\lim_{x \to -\infty} x^{x} = \infty
More at x→-oo
The graph
Limit of the function x^x
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