2. Пользуясь свойствами пределов, вычислите:

a) lim_{n->∞} (7n + 3)/(5n - 12) = lim_{n->∞} (7 + 3/n)/(5 - 12/n) = 7/5. b) lim_{n->∞} (2n^2 + n - 10)/(n^3 + 12n + 20) = lim_{n->∞} (2/n + 1/n^2 - 10/n^3)/(1 + 12/n^2 + 20/n^3) = 0. в) lim_{n->∞} (6n + 5)/(2n - 3) = lim_{n->∞} (6 + 5/n)/(2 - 3/n) = 6/2 = 3. г) lim_{n->∞} (-3n^3 + 4n - 10)/(5n^2 + n + 21) = lim_{n->∞} (-3/n + 4/n^2 - 10/n^3)/(5 + 1/n + 21/n^2) = 0. д) lim_{n->∞} (sqrt(n^2 + n) - sqrt(n^2 + 11)) = lim_{n->∞} (n(1 + 1/n)^(1/2) - n(1 + 11/n^2)^(1/2)) = lim_{n->∞} (n[(1 + 1/n)^(1/2) - (1 + 11/n^2)^(1/2)]) = lim_{n->∞} [(1/2n - 11/2n^3)] = 0. е) lim_{n->∞} (1 + 1/(3n))^n = e^(1/3).