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x*cot(x)
Limit of the function/ x*cot(x)

Limit of the function x*cot(x)

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You have entered [src] 
 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
Plot the graph
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
$$\lim_{x \to 2^-}\left(x \cot{\left(x \right)}\right) = \frac{2}{\tan{\left(2 \right)}}$$
More at x→2 from the left
$$\lim_{x \to 2^+}\left(x \cot{\left(x \right)}\right) = \frac{2}{\tan{\left(2 \right)}}$$
$$\lim_{x \to \infty}\left(x \cot{\left(x \right)}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(x \cot{\left(x \right)}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \cot{\left(x \right)}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \cot{\left(x \right)}\right) = \frac{1}{\tan{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \cot{\left(x \right)}\right) = \frac{1}{\tan{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \cot{\left(x \right)}\right)$$
More at x→-oo
Numerical answer [src] 
-0.915315108720572
-0.915315108720572
The graph
Limit of the function x*cot(x)
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