Limits at infinity describe function behavior as x→∞ or x→-∞. For rational functions, highest degree terms dominate. lim(x→∞) [(3x² + 2x)/(5x² - 1)] = 3/5 (divide by x²). If numerator degree > denominator, limit = ±∞. If denominator degree > numerator, limit = 0. Horizontal asymptotes: y = L if lim(x→±∞) f(x) = L. For exponential: lim(x→∞) eˣ = ∞, lim(x→-∞) eˣ = 0. Solving: Identify degrees; divide by highest power; simplify. Example: lim(x→∞) [(2x + 5)/(x² + 1)] = 0 (denominator dominates). Exam tip: Understand end behavior from asymptotes. Distinguish between limits at infinity and at finite points.