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Giải bài 1.24 trang 19 sách bài tập toán 12 - Kết nối tri thức

Cho hàm số (y = fleft( x right)) có bảng biến thiên như sau: Hãy tìm các tiệm cận đứng và tiệm cận ngang của đồ thị hàm số đã cho.

🥀Tổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Hoá - Sinh - Sử - Địa
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Đề bài

Cho hàm số \(y = f\left( x \right)\) có bảng biến thiên như sau:

Hãy tìm các tiệm cận đứng và tiệm cận ngang của đồ thị hàm số đã cho.

Phương pháp giải - Xem chi tiết

Quan sát bảng biến thiên, tính các giới hạn theo định nghĩa tiệm cận để tìm các tiệm cận đó. Ví dụ tìm tiệm cận đứng thì tìm giới hạn tại đâu có kết quả bằng \(\infty \), tìm tiệm cận đứng thì tìm giá trị \(y\) khi \(x \to \infty \), kết quả có trên hình vẽ bảng biến thiên.

Lời giải chi tiết

Từ bảng biến thiên ta thấy \(\mathop {\lim }\limits_{x \to {2^ - }} f\left( x \right) =  + \infty \). Do đó đồ thị có tiệm cận đứng là đường thẳng \(x = 2\). \(\mathop {\lim }\limits_{x \to  + \infty } f\left( x \right) = 3\) suy ra đường thẳng \(y = 3\) là tiệm cận ngang của đồ thị hàm số.

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