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Giải bài 5.15 trang 83 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Cho hàm số \(f\left( x \right) = \frac{{\sqrt {{x^2} - x + 2} }}{x}\).

ꦜTổng 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 \(f\left( x \right) = \frac{{\sqrt {{x^2} - x + 2} }}{x}\). Tính a) \(\mathop {\lim }\limits_{x \to  + \infty } f\left( x \right);\)                              b) \(\mathop {\lim }\limits_{x \to  - \infty } f\left( x \right);\)

Phương pháp giải - Xem chi tiết

- 💜Các quy tắc tính giới hạn hữu hạn tại một điểm cũng đúng cho giới hạn hữu hạn tại vô cực.

- Với c là hằng số, ta có: \(\mathop {\lim }\limits_{x \to  + \infty } c = c,\mathop {\lim }\limits_{x \to  - \infty } c = c\) - Với k là một số nguyên dương, ta có: \(\mathop {\lim }\limits_{x \to  + \infty } \frac{1}{{{x^k}}} = 0,\mathop {\lim }\limits_{x \to  - \infty } \frac{1}{{{x^k}}} = 0\)

Lời giải chi tiết

a) \(\mathop {\lim }\limits_{x \to  + \infty } f\left( x \right) = \mathop {\lim }\limits_{x \to  + \infty } \frac{{\sqrt {{x^2} - x + 2} }}{x} = \mathop {\lim }\limits_{x \to  + \infty } \frac{{\sqrt {1 - \frac{1}{x} + \frac{2}{{{x^2}}}} }}{1} = 1\)b) \(\mathop {\lim }\limits_{x \to  - \infty } f\left( x \right) = \mathop {\lim }\limits_{x \to  - \infty } \frac{{\sqrt {{x^2} - x + 2} }}{x} = \mathop {\lim }\limits_{x \to  - \infty } \frac{{ - \sqrt {1 - \frac{1}{x} + \frac{2}{{{x^2}}}} }}{1} =  - 1\)

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

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