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Giải bài 5.1 trang 77 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Tính các giới hạn sau:

ꦛTổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Tính các giới hạn sau: a) \(\mathop {\lim }\limits_{n \to  + \infty } \frac{{{n^2} + 1}}{{2{n^2} + n + 2}};\)          b) \(\mathop {\lim }\limits_{n \to  + \infty } \frac{{{2^n} + 3}}{{1 + {3^n}}}.\)

Phương pháp giải - Xem chi tiết

Để tính giới hạn của dãy số dạng phân thức, ta chia cả tử thức và mẫu thức cho lũy thừa cao nhất của n, rồi áp dụng các quy tắc tính giới hạn.

Lời giải chi tiết

a) \(\mathop {\lim }\limits_{n \to  + \infty } \frac{{{n^2} + 1}}{{2{n^2} + n + 2}} = \mathop {\lim }\limits_{n \to  + \infty } \frac{{1 + \frac{1}{{{n^2}}}}}{{2 + \frac{1}{n} + \frac{2}{{{n^2}}}}} = \frac{1}{2}\)          b) \(\mathop {\lim }\limits_{n \to  + \infty } \frac{{{2^n} + 3}}{{1 + {3^n}}} = \mathop {\lim }\limits_{n \to  + \infty } \frac{{{{\left( {\frac{2}{3}} \right)}^n} + {{\left( {\frac{1}{3}} \right)}^{n - 1}}}}{{{{\left( {\frac{1}{3}} \right)}^n} + 1}} = 0\)

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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