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lim coth(x) x->oo

$$\lim_{x \to \infty} \coth{\left(x \right)}$$

Limit(coth(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

Other limits x→0, -oo, +oo, 1

$$\lim_{x \to \infty} \coth{\left(x \right)} = 1$$

$$\lim_{x \to 0^-} \coth{\left(x \right)} = -\infty$$

More at x→0 from the left

$$\lim_{x \to 0^+} \coth{\left(x \right)} = \infty$$

More at x→0 from the right

$$\lim_{x \to 1^-} \coth{\left(x \right)} = \coth{\left(1 \right)}$$

More at x→1 from the left

$$\lim_{x \to 1^+} \coth{\left(x \right)} = \coth{\left(1 \right)}$$

More at x→1 from the right

$$\lim_{x \to -\infty} \coth{\left(x \right)} = -1$$

More at x→-oo

$$\lim_{x \to 0^-} \coth{\left(x \right)} = -\infty$$

More at x→0 from the left

$$\lim_{x \to 0^+} \coth{\left(x \right)} = \infty$$

More at x→0 from the right

$$\lim_{x \to 1^-} \coth{\left(x \right)} = \coth{\left(1 \right)}$$

More at x→1 from the left

$$\lim_{x \to 1^+} \coth{\left(x \right)} = \coth{\left(1 \right)}$$

More at x→1 from the right

$$\lim_{x \to -\infty} \coth{\left(x \right)} = -1$$

More at x→-oo

The graph