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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+
$$\lim_{x \to 0^+}\left(x \operatorname{acot}{\left(x \right)}\right)$$ 
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
Plot the graph
Rapid solution [src] 
0
$$0$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(x \operatorname{acot}{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \operatorname{acot}{\left(x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(x \operatorname{acot}{\left(x \right)}\right) = 1$$
More at x→oo
$$\lim_{x \to 1^-}\left(x \operatorname{acot}{\left(x \right)}\right) = \frac{\pi}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \operatorname{acot}{\left(x \right)}\right) = \frac{\pi}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \operatorname{acot}{\left(x \right)}\right) = 1$$
More at x→-oo
One‐sided limits [src] 
 lim (x*acot(x))
x->0+
$$\lim_{x \to 0^+}\left(x \operatorname{acot}{\left(x \right)}\right)$$ 
0
$$0$$ 
= 2.86734555729065e-32
 lim (x*acot(x))
x->0-
$$\lim_{x \to 0^-}\left(x \operatorname{acot}{\left(x \right)}\right)$$ 
0
$$0$$ 
= 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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