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