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

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

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         tan(x)   
 lim acot      (x)
x->0+
lim⁡x→0+acot⁡tan⁡(x)(x)\lim_{x \to 0^+} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)} 
Limit(acot(x)^tan(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
02468-8-6-4-2-1010050000000000000000000
Plot the graph
Rapid solution [src] 
1
11
Expand and simplify
One‐sided limits [src] 
         tan(x)   
 lim acot      (x)
x->0+
lim⁡x→0+acot⁡tan⁡(x)(x)\lim_{x \to 0^+} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)} 
1
11 
= 1.0
         tan(x)   
 lim acot      (x)
x->0-
lim⁡x→0−acot⁡tan⁡(x)(x)\lim_{x \to 0^-} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)} 
1
11 
= (1.0 + 7.25708536419871e-27j)
= (1.0 + 7.25708536419871e-27j)
Other limits x→0, -oo, +oo, 1
lim⁡x→0−acot⁡tan⁡(x)(x)=1\lim_{x \to 0^-} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)} = 1
More at x→0 from the left
lim⁡x→0+acot⁡tan⁡(x)(x)=1\lim_{x \to 0^+} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)} = 1
lim⁡x→∞acot⁡tan⁡(x)(x)\lim_{x \to \infty} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)}
More at x→oo
lim⁡x→1−acot⁡tan⁡(x)(x)=πtan⁡(1)22tan⁡(1)\lim_{x \to 1^-} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)} = \frac{\pi^{\tan{\left(1 \right)}}}{2^{2 \tan{\left(1 \right)}}}
More at x→1 from the left
lim⁡x→1+acot⁡tan⁡(x)(x)=πtan⁡(1)22tan⁡(1)\lim_{x \to 1^+} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)} = \frac{\pi^{\tan{\left(1 \right)}}}{2^{2 \tan{\left(1 \right)}}}
More at x→1 from the right
lim⁡x→−∞acot⁡tan⁡(x)(x)\lim_{x \to -\infty} \operatorname{acot}^{\tan{\left(x \right)}}{\left(x \right)}
More at x→-oo
Numerical answer [src] 
1.0
1.0
The graph
Limit of the function acot(x)^tan(x)
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