Решение
a) lim x--> ∞ 5/(3 + x²) = 5/(3 + ∞) = 5/∞ = 0
б) lim x--> ∞ 4x/(5-x) = [∞/∞] = lim x--> ∞ [(4x)/x] / (5/x - x/x) =
= lim x--> ∞ 4 / (5/x - 1) = 4 / (5/∞ - 1) = 4 / (0 - 1) = - 4
в) lim x--> ∞ (3x² - 5x + 4)/(x² - 2x + 3) = [∞/∞] =
lim x--> ∞ (3x²/x² - 5x/x² + 4/x²)/(x²/x² - 2x/x² + 3/x²) =
= lim x--> ∞ (3 - 5/x + 4/x²)/(1 - 2/x + 3/x²) = (3 - 5/∞ + 4/∞²)/(1 - 2/∞ + 3/∞²) =
= (3 - 0 +0)/(1 - 0 + 0) = 3