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Bài 5.7 trang 118 SGK Toán 11 tập 1 - Kết nối tri thức

Cho hai hàm số (fleft( x right) = frac{{{x^2} - 1}}{{x - 1}}) và g(x) = x + 1. Khẳng định nào sau đây là đúng?

🎃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

Cho hai hàm số \(f\left( x \right) = \frac{{{x^2} - 1}}{{x - 1}}\) và g(x) = x + 1. Khẳng định nào sau đây là đúng? a) f(x) = g(x); b) \(\mathop {\lim }\limits_{x \to 1} f\left( x \right) = \mathop {\lim }\limits_{x \to 1} g\left( x \right)\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

a) Kiểm tra xem ĐKXĐ của 2 hàm số có giống nhau không. b) Tính giới hạn của hai hàm số.

Lời giải chi tiết

+) Biểu thức f(x) có nghĩa khi x – 1 ≠ 0 ⇔ x ≠ 1.Ta có: \(f\left( x \right) = \frac{{{x^2} - 1}}{{x - 1}} = \frac{{\left( {x - 1} \right)\left( {x + 1} \right)}}{{x - 1}} = x + 1\), với mọi x ≠ 1.Biểu thức g(x) = x + 1 có nghĩa với mọi x.Do đó, điều kiện xác định của hai hàm số f(x) và g(x) khác nhau, vậy khẳng định a) là sai.+) Ta có: \(\mathop {\lim }\limits_{x \to 1} f\left( x \right) = \mathop {\lim }\limits_{x \to 1} \frac{{{x^2} - 1}}{{x - 1}} = \mathop {\lim }\limits_{x \to 1} \left( {x + 1} \right) = 1 + 1 = 2\);Vậy \(\mathop {\lim }\limits_{x \to 1} f\left( x \right) = \mathop {\lim }\limits_{x \to 1} g\left( x \right)\) nên khẳng định b) là đúng.

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