$$\lim_{x \to \infty}\left(- 2 \cos{\left(x \right)}\right) = \left\langle -2, 2\right\rangle$$
$$\lim_{x \to 0^-}\left(- 2 \cos{\left(x \right)}\right) = -2$$
More at x→0 from the left$$\lim_{x \to 0^+}\left(- 2 \cos{\left(x \right)}\right) = -2$$
More at x→0 from the right$$\lim_{x \to 1^-}\left(- 2 \cos{\left(x \right)}\right) = - 2 \cos{\left(1 \right)}$$
More at x→1 from the left$$\lim_{x \to 1^+}\left(- 2 \cos{\left(x \right)}\right) = - 2 \cos{\left(1 \right)}$$
More at x→1 from the right$$\lim_{x \to -\infty}\left(- 2 \cos{\left(x \right)}\right) = \left\langle -2, 2\right\rangle$$
More at x→-oo