Limit of the function acot(x)/x

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     /acot(x)\
 lim |-------|
x->oo\   x   /

\lim_{x \to \infty}\left(\frac{\operatorname{acot}{\left(x \right)}}{x}\right)

Limit(acot(x)/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

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Rapid solution [src]

0

Expand and simplify

Other limits x→0, -oo, +oo, 1

\lim_{x \to \infty}\left(\frac{\operatorname{acot}{\left(x \right)}}{x}\right) = 0

\lim_{x \to 0^-}\left(\frac{\operatorname{acot}{\left(x \right)}}{x}\right) = \infty

\lim_{x \to 0^+}\left(\frac{\operatorname{acot}{\left(x \right)}}{x}\right) = \infty

\lim_{x \to 1^-}\left(\frac{\operatorname{acot}{\left(x \right)}}{x}\right) = \frac{\pi}{4}

\lim_{x \to 1^+}\left(\frac{\operatorname{acot}{\left(x \right)}}{x}\right) = \frac{\pi}{4}

\lim_{x \to -\infty}\left(\frac{\operatorname{acot}{\left(x \right)}}{x}\right) = 0

The graph