Mister Exam

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

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     /      /x \\
 lim |x*acot|--||
n->oo|      | 2||
     \      \n //

\lim_{n \to \infty}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right)

Limit(x*acot(x/n^2), n, 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

Rapid solution [src]

pi*x
----
 2

\frac{\pi x}{2}

Expand and simplify

Other limits n→0, -oo, +oo, 1

\lim_{n \to \infty}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = \frac{\pi x}{2}

\lim_{n \to 0^-}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = x \operatorname{acot}{\left(\tilde{\infty} x \right)}

\lim_{n \to 0^+}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = x \operatorname{acot}{\left(\tilde{\infty} x \right)}

\lim_{n \to 1^-}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = x \operatorname{acot}{\left(x \right)}

\lim_{n \to 1^+}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = x \operatorname{acot}{\left(x \right)}

\lim_{n \to -\infty}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = \frac{\pi x}{2}