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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] 
 lim (x*acot(x))
x->0+
lim⁡x→0+(xacot⁡(x))\lim_{x \to 0^+}\left(x \operatorname{acot}{\left(x \right)}\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
02468-8-6-4-2-101002
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(xacot⁡(x))=0\lim_{x \to 0^-}\left(x \operatorname{acot}{\left(x \right)}\right) = 0
More at x→0 from the left
lim⁡x→0+(xacot⁡(x))=0\lim_{x \to 0^+}\left(x \operatorname{acot}{\left(x \right)}\right) = 0
lim⁡x→∞(xacot⁡(x))=1\lim_{x \to \infty}\left(x \operatorname{acot}{\left(x \right)}\right) = 1
More at x→oo
lim⁡x→1−(xacot⁡(x))=π4\lim_{x \to 1^-}\left(x \operatorname{acot}{\left(x \right)}\right) = \frac{\pi}{4}
More at x→1 from the left
lim⁡x→1+(xacot⁡(x))=π4\lim_{x \to 1^+}\left(x \operatorname{acot}{\left(x \right)}\right) = \frac{\pi}{4}
More at x→1 from the right
lim⁡x→−∞(xacot⁡(x))=1\lim_{x \to -\infty}\left(x \operatorname{acot}{\left(x \right)}\right) = 1
More at x→-oo
One‐sided limits [src] 
 lim (x*acot(x))
x->0+
lim⁡x→0+(xacot⁡(x))\lim_{x \to 0^+}\left(x \operatorname{acot}{\left(x \right)}\right) 
0
00 
= 2.86734555729065e-32
 lim (x*acot(x))
x->0-
lim⁡x→0−(xacot⁡(x))\lim_{x \to 0^-}\left(x \operatorname{acot}{\left(x \right)}\right) 
0
00 
= 2.86734555729065e-32
= 2.86734555729065e-32
Numerical answer [src] 
2.86734555729065e-32
2.86734555729065e-32
The graph
Limit of the function x*acot(x)
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