$$\lim_{n \to \infty} \cot{\left(n \right)} = \left\langle -\infty, \infty\right\rangle$$ $$\lim_{n \to 0^-} \cot{\left(n \right)} = -\infty$$ More at n→0 from the left $$\lim_{n \to 0^+} \cot{\left(n \right)} = \infty$$ More at n→0 from the right $$\lim_{n \to 1^-} \cot{\left(n \right)} = \cot{\left(1 \right)}$$ More at n→1 from the left $$\lim_{n \to 1^+} \cot{\left(n \right)} = \cot{\left(1 \right)}$$ More at n→1 from the right $$\lim_{n \to -\infty} \cot{\left(n \right)} = \left\langle -\infty, \infty\right\rangle$$ More at n→-oo