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Bài 5.21 trang 123 SGK Toán 11 tập 1 - Kết nối tri thức

Cho hàm số (fleft( x right) = sqrt {x + 1} - sqrt {x + 2} ). Mệnh đề đúng là A. (mathop {lim }limits_{x to + infty } fleft( x right) = - infty ) B. (mathop {lim }limits_{x to + infty } fleft( x right) = 0) C. (mathop {lim }limits_{x to + infty } fleft( x right) = - 1) D. (mathop {lim }limits_{x to + infty } fleft( x right) = - frac{1}{2})

ꦬTổng 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

Cho hàm số \(f\left( x \right) = \sqrt {x + 1}  - \sqrt {x + 2} \). Mệnh đề đúng là A. \(\mathop {\lim }\limits_{x \to  + \infty } f\left( x \right) =  - \infty \)                      B. \(\mathop {\lim }\limits_{x \to  + \infty } f\left( x \right) = 0\)              C. \(\mathop {\lim }\limits_{x \to  + \infty } f\left( x \right) =  - 1\)     D. \(\mathop {\lim }\limits_{x \to  + \infty } f\left( x \right) =  - \frac{1}{2}\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Đây là giớ hạn dạng \(\frac{0}{0}\), để khử dạng này ta nhân liên hợp. Sau đó, ta chia cả tử và mẫu cho lũy thừa cao nhất của n, rồi áp dụng quy tắc tính giới hạn.

Lời giải chi tiết

Ta có:\(\mathop {\lim }\limits_{x \to  + \infty } \left( {\sqrt {x + 1}  - \sqrt {x + 2} } \right) = \mathop {\lim }\limits_{x \to  + \infty } \frac{{x + 1 - x - 2}}{{\sqrt {x + 1}  + \sqrt {x + 2} }} = \mathop {\lim }\limits_{x \to  + \infty } \frac{{ - 1}}{{\sqrt {x + 1}  + \sqrt {x + 2} }} = \mathop {\lim }\limits_{x \to  + \infty } \frac{{\frac{{ - 1}}{x}}}{{\sqrt {1 + \frac{1}{x}}  + \sqrt {1 + \frac{2}{x}} }} = \frac{0}{2} = 0\)Đáp án: B

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

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