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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+
$$\lim_{x \to 0^+} x^{e}$$ 
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
Plot the graph
Rapid solution [src] 
0
$$0$$
Expand and simplify
One‐sided limits [src] 
      E
 lim x 
x->0+
$$\lim_{x \to 0^+} x^{e}$$ 
0
$$0$$ 
= 5.53639714030193e-10
      E
 lim x 
x->0-
$$\lim_{x \to 0^-} x^{e}$$ 
0
$$0$$ 
= (-3.63290818199403e-10 + 4.35999625826301e-10j)
= (-3.63290818199403e-10 + 4.35999625826301e-10j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} x^{e} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} x^{e} = 0$$
$$\lim_{x \to \infty} x^{e} = \infty$$
More at x→oo
$$\lim_{x \to 1^-} x^{e} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x^{e} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} x^{e} = \infty \operatorname{sign}{\left(\left(-1\right)^{e} \right)}$$
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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