• We study the behaviour of a function when x increases without bound (x → ∞), or when x decreases without bound (x → −∞). ∞ is not a number.
• It shows that x keeps growing with no end.
• The key idea is that a fraction whose denominator grows without bound approaches zero. Therefore:

limx → ∞ 1/x = 0

• lim_{x → ∞} 1/x² = 0, and in general lim_{x → ∞} 1/xⁿ = 0 for any positive integer n.
• lim_{x → −∞} 1/x = 0 as well.