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Giải bài 5.45 trang 89 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Tìm a là số thực thỏa mãn \(\mathop {\lim }\limits_{x \to + \infty } \left( {\frac{{2{x^2} + 1}}{{{x^2} + 2x + 3}} + {a^2} + 3a} \right) = 0\).

💜Tổng 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

Tìm a𝐆 là số thực thỏa mãn \(\mathop {\lim }\limits_{x \to  + \infty } \left( {\frac{{2{x^2} + 1}}{{{x^2} + 2x + 3}} + {a^2} + 3a} \right) = 0\).

Phương pháp giải - Xem chi tiết

Dựa vào quy tắc tính giới hạn, ta tính ra \(\mathop {\lim }\limits_{x \to  + \infty } \left( {\frac{{2{x^2} + 1}}{{{x^2} + 2x + 3}} + {a^2} + 3a} \right) = 0\) thì a bằng bao nhiêu (quy về dạng giải phương trình ẩn a).

Lời giải chi tiết

Ta có \(\mathop {\lim }\limits_{x \to  + \infty } \left( {\frac{{2{x^2} + 1}}{{{x^2} + 2x + 3}} + {a^2} + 3a} \right) = 2 + {a^2} + 3a = 0.\)Do đó  \(a =  - 1\) hoặc \(a =  - 2\).

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

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