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

Limit of the function x^acot(x)

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The solution

You have entered [src] 
      acot(x)
 lim x       
x->0+
$$\lim_{x \to 0^+} x^{\operatorname{acot}{\left(x \right)}}$$ 
Limit(x^acot(x), 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] 
      acot(x)
 lim x       
x->0+
$$\lim_{x \to 0^+} x^{\operatorname{acot}{\left(x \right)}}$$ 
0
$$0$$ 
= 3.43151112916385e-6
      acot(x)
 lim x       
x->0-
$$\lim_{x \to 0^-} x^{\operatorname{acot}{\left(x \right)}}$$ 
       /      2 \
       | -I*pi  |
       | -------|
       |    2   |
oo*sign\e       /
$$\infty \operatorname{sign}{\left(e^{- \frac{i \pi^{2}}{2}} \right)}$$ 
= (512.697493393348 + 2508.48953447685j)
= (512.697493393348 + 2508.48953447685j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} x^{\operatorname{acot}{\left(x \right)}} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} x^{\operatorname{acot}{\left(x \right)}} = 0$$
$$\lim_{x \to \infty} x^{\operatorname{acot}{\left(x \right)}} = 1$$
More at x→oo
$$\lim_{x \to 1^-} x^{\operatorname{acot}{\left(x \right)}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x^{\operatorname{acot}{\left(x \right)}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} x^{\operatorname{acot}{\left(x \right)}} = 1$$
More at x→-oo
Numerical answer [src] 
3.43151112916385e-6
3.43151112916385e-6
The graph
Limit of the function x^acot(x)
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