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Limit of the function/ x^y

Limit of the function x^y

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The solution

You have entered [src] 
      y
 lim x 
y->0+
lim⁡y→0+xy\lim_{y \to 0^+} x^{y} 
Limit(x^y, y, 0)
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
Rapid solution [src] 
1
11
Expand and simplify
One‐sided limits [src] 
      y
 lim x 
y->0+
lim⁡y→0+xy\lim_{y \to 0^+} x^{y} 
1
11 
      y
 lim x 
y->0-
lim⁡y→0−xy\lim_{y \to 0^-} x^{y} 
1
11 
1
Other limits y→0, -oo, +oo, 1
lim⁡y→0−xy=1\lim_{y \to 0^-} x^{y} = 1
More at y→0 from the left
lim⁡y→0+xy=1\lim_{y \to 0^+} x^{y} = 1
lim⁡y→∞xy\lim_{y \to \infty} x^{y}
More at y→oo
lim⁡y→1−xy=x\lim_{y \to 1^-} x^{y} = x
More at y→1 from the left
lim⁡y→1+xy=x\lim_{y \to 1^+} x^{y} = x
More at y→1 from the right
lim⁡y→−∞xy\lim_{y \to -\infty} x^{y}
More at y→-oo
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