Задача 1
Задача 2
Для начала неплохо бы ознакомиться с теорией: |
| Отрывок из книги "Математический анализ. Дифференциальное исчисление. Виленкин Н.Я., Куницкая Е.С., Мордкович А.Г.", стр. 129 |
Также полезно ознакомиться с вычислением пределов:
Wolfram|Alpha® по-русски: Вычисление пределов в Wolfram|Alpha
Далее приведено решение:
limit sqrt(log(4,n)) / log(2,log(2,n)), n->+oo
limit (log(2,n))^2 / log(3,n), n->+oo
limit (log(2,n))^2 / log(2,log(2,n)), n->+oo
limit sqrt(n) / log(2,log(2,n)), n->+oo
limit sqrt(n) / (log(2,n))^2, n->+oo
limit (n/log(5,n)) / (log(2,n))^2, n->+oo
limit (log(2,n!)) / (log(2,n))^2, n->+oo
limit (log(2,n!)) / (n/log(5,n)), n->+oo
limit (3^log(2,n)) / (log(2,n!)), n->+oo
limit (n^2) / (log(2,n!)), n->+oo
limit (7^log(2,n)) / (n^2), n->+oo
limit ((log(2,n))^log(2,n)) / (log(2,n!)), n->+oo
limit ((log(2,n))^log(2,n)) / (7^log(2,n)), n->+oo
limit (n^(log(2,n))) / ((log(2,n))^log(2,n)), n->+oo
limit (n^sqrt(n)) / (log(2,n!)), n->+oo
limit (2^n) / (n^sqrt(n)), n->+oo
limit (4^n) / ((log(2,n))^log(2,n)), n->+oo
limit (4^n) / (2^n), n->+oo
limit (2^(3n)) / (log(2,n!)), n->+oo
limit (2^(3n)) / ((log(2,n))^log(2,n)), n->+oo
limit (2^(3n)) / (4^n), n->+oo
limit (n!) / (log(2,n!)) , n->+oo
limit (n!) / ((log(2,n))^log(2,n)), n->+oo
limit (n!) / (2^(3n)) , n->+oo
limit (2^(2^n)) / (n!) , n->+oo
Задача 4
limit (n!) / (2^n) , n->oo = ∞
limit (2^n) / (n!) , n->oo = 0
limit (10*log(2,n)) / (log(2,n)^2) , n->oo = 0
limit (log(2,n)^2) / (10*log(2,n)) , n->oo = ∞
limit (2^n) / (2^(n+1)) , n->oo = 1/2
limit (2^(n+1)) / (2^n) , n->oo = 2
limit (100*n*log(2,n)) / (n+(log(2,n)^2)) , n->oo = ∞
limit (n+(log(2,n)^2)) / (100*n*log(2,n)) , n->oo = 0
limit (sqrt(n)) / (log(2,n)^3) , n->oo = ∞
limit (log(2,n)^3) / (sqrt(n)) , n->oo = 0
limit ((n^2)/log(4,n)) / (n*(log(3,n)^2)) , n->oo = ∞
limit (n*(log(3,n)^2)) / ((n^2)/log(4,n)) , n->oo = 0
Задача 5
limit (n^3) / (log(n)n^2) , n->oo
limit (n^log(2,5)) / (n^log(2,3)) , n->oo
limit (log(n)n^2) / (n^2) , n->oo
limit (n^2) / (log(n)n) , n->oo
limit (n^log(2,3)) / (n^log(4,5)) , n->oo
limit (n^log(4,5)) / (n^log(3,2)) , n->oo
limit (log(n)n) / (log(n)) , n->oo
Задача 6
T(n)=2T(n−1)+1, T(1)=1
Задача 7
limit (2^n) / (3^((3n)/4)) , n->oo = 0limit (2^n) / (7^log(5,n)) , n->oo = ∞
limit (7^log(5,n)) / (4^log(2,n)) , n->oo = 0
limit 2^n / (4^log(2,n)) , n->oo = ∞
limit (7^log(5,n)) / (log(3,n)n^2) , n->oo = 0
limit (4^log(2,n)) / (log(3,n)n^2) , n->oo = 0
limit 2^n / (log(3,n)n^2) , n->oo = ∞
limit (7^log(5,n)) / (n/log(2,n)) , n->oo = ∞
limit (7^log(5,n)) / (n^3/log(2,n)^5) , n->oo = 0
limit (4^log(2,n)) / (n^3/log(2,n)^5) , n->oo = 0
limit (log(3,n)n^2) / (n^3/log(2,n)^5) , n->oo = 0
limit 2^n / (n^3/log(2,n)^5) , n->oo = ∞
limit (n/log(2,n)) / n , n->oo = 0
limit (7^log(5,n)) / n , n->oo = ∞
Задача 8
limit e^x / e^(log(e,x))^2 as x->+oo = ∞limit e^sqrt(x) / e^(log(e,x))^2 as x->+oo = ∞
Задача 9
limit e^x^2 / e^x as x->+oo = ∞limit e^x / x^ln(x) as x->+oo = ∞
