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