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Limit of the function x*cot(x)

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 lim (x*cot(x))
x->2+

\lim_{x \to 2^+}\left(x \cot{\left(x \right)}\right)

Limit(x*cot(x), x, 2)

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]

  2   
------
tan(2)

\frac{2}{\tan{\left(2 \right)}}

Expand and simplify

One‐sided limits [src]

 lim (x*cot(x))
x->2+

\lim_{x \to 2^+}\left(x \cot{\left(x \right)}\right)

  2   
------
tan(2)

\frac{2}{\tan{\left(2 \right)}}

= -0.915315108720572

 lim (x*cot(x))
x->2-

\lim_{x \to 2^-}\left(x \cot{\left(x \right)}\right)

  2   
------
tan(2)

\frac{2}{\tan{\left(2 \right)}}

= -0.915315108720572

= -0.915315108720572

Other limits x→0, -oo, +oo, 1

\lim_{x \to 2^-}\left(x \cot{\left(x \right)}\right) = \frac{2}{\tan{\left(2 \right)}}

\lim_{x \to 2^+}\left(x \cot{\left(x \right)}\right) = \frac{2}{\tan{\left(2 \right)}}

\lim_{x \to \infty}\left(x \cot{\left(x \right)}\right)

\lim_{x \to 0^-}\left(x \cot{\left(x \right)}\right) = 1

\lim_{x \to 0^+}\left(x \cot{\left(x \right)}\right) = 1

\lim_{x \to 1^-}\left(x \cot{\left(x \right)}\right) = \frac{1}{\tan{\left(1 \right)}}

\lim_{x \to 1^+}\left(x \cot{\left(x \right)}\right) = \frac{1}{\tan{\left(1 \right)}}

\lim_{x \to -\infty}\left(x \cot{\left(x \right)}\right)

Numerical answer [src]

-0.915315108720572

-0.915315108720572

The graph