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acot(2*x)
Limit of the function/ acot(2*x)

Limit of the function acot(2*x)

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The solution

You have entered [src] 
 lim acot(2*x)
x->oo
lim⁡x→∞acot⁡(2x)\lim_{x \to \infty} \operatorname{acot}{\left(2 x \right)} 
Limit(acot(2*x), x, oo, dir='-')
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
02468-8-6-4-2-10105-5
Plot the graph
Rapid solution [src] 
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Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞acot⁡(2x)=0\lim_{x \to \infty} \operatorname{acot}{\left(2 x \right)} = 0
lim⁡x→0−acot⁡(2x)=−π2\lim_{x \to 0^-} \operatorname{acot}{\left(2 x \right)} = - \frac{\pi}{2}
More at x→0 from the left
lim⁡x→0+acot⁡(2x)=π2\lim_{x \to 0^+} \operatorname{acot}{\left(2 x \right)} = \frac{\pi}{2}
More at x→0 from the right
lim⁡x→1−acot⁡(2x)=acot⁡(2)\lim_{x \to 1^-} \operatorname{acot}{\left(2 x \right)} = \operatorname{acot}{\left(2 \right)}
More at x→1 from the left
lim⁡x→1+acot⁡(2x)=acot⁡(2)\lim_{x \to 1^+} \operatorname{acot}{\left(2 x \right)} = \operatorname{acot}{\left(2 \right)}
More at x→1 from the right
lim⁡x→−∞acot⁡(2x)=0\lim_{x \to -\infty} \operatorname{acot}{\left(2 x \right)} = 0
More at x→-oo
The graph
Limit of the function acot(2*x)
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