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Limit of the function/ x^e

Limit of the function x^e

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The solution

You have entered [src] 
      E
 lim x 
x->0+
lim⁡x→0+xe\lim_{x \to 0^+} x^{e} 
Limit(x^E, x, 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
The graph
02468-8-6-4-2-101001000
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
One‐sided limits [src] 
      E
 lim x 
x->0+
lim⁡x→0+xe\lim_{x \to 0^+} x^{e} 
0
00 
= 5.53639714030193e-10
      E
 lim x 
x->0-
lim⁡x→0−xe\lim_{x \to 0^-} x^{e} 
0
00 
= (-3.63290818199403e-10 + 4.35999625826301e-10j)
= (-3.63290818199403e-10 + 4.35999625826301e-10j)
Other limits x→0, -oo, +oo, 1
lim⁡x→0−xe=0\lim_{x \to 0^-} x^{e} = 0
More at x→0 from the left
lim⁡x→0+xe=0\lim_{x \to 0^+} x^{e} = 0
lim⁡x→∞xe=∞\lim_{x \to \infty} x^{e} = \infty
More at x→oo
lim⁡x→1−xe=1\lim_{x \to 1^-} x^{e} = 1
More at x→1 from the left
lim⁡x→1+xe=1\lim_{x \to 1^+} x^{e} = 1
More at x→1 from the right
lim⁡x→−∞xe=∞sign⁡((−1)e)\lim_{x \to -\infty} x^{e} = \infty \operatorname{sign}{\left(\left(-1\right)^{e} \right)}
More at x→-oo
Numerical answer [src] 
5.53639714030193e-10
5.53639714030193e-10
The graph
Limit of the function x^e
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