Limit properties and theorems: (1) Limit of constant = constant; (2) Limit of sum = sum of limits; (3) Limit of product = product of limits; (4) Limit of quotient = quotient of limits (if denominator ≠ 0); (5) Squeeze theorem: If g(x) ≤ f(x) ≤ h(x) and lim g = lim h = L, then lim f = L. Standard limits: lim(x→0) [sin x / x] = 1; lim(x→0) [(1+x)^(1/x)] = e; lim(x→∞) [1 + 1/x]^x = e. Application: Solving complex limits using properties. Example: lim(x→1) [(x² - 1)/(x-1)] = lim(x→1) [(x+1)(x-1)/(x-1)] = lim(x→1) (x+1) = 2. Exam tip: Simplify before substituting. Use standard limits efficiently.