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Bài 1.28 trang 40 SGK Toán 11 tập 1 - Kết nối tri thức

Trong các hàm số sau đây, hàm số nào là hàm tuần hoàn?

𝐆Tổng 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

Trong các hàm số sau đây, hàm số nào là hàm tuần hoàn? A. \(y = \tan x + x\)     B. \(y = {x^2} + 1\)               C. \(y = \cot x\)                       D. \(y = \frac{{\sin x}}{x}\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Xét tính tuần hoàn của hàm số - Xét hàm số \(y = f\left( x \right)\), tập xác định là D - Với mọi \(x \in D\), ta có \(x - {T_0}\; \in D\) và \(x + {T_0} \in D\;\) Chỉ ra \(f\left( {x + {T_0}} \right) = f\left( x \right)\; = f\left( {x - {T_0}} \right)\) Vậy hàm số \(y = f\left( x \right)\) tuần hoàn

Lời giải chi tiết

Hàm \(y = \cot x\) là hàm tuần hoàn với chu kì \(T = \pi \) do :- Tập xác định là \(D = R\backslash \left\{ {k\pi ;k \in Z} \right\}\)- Với mọi \(x \in D\), ta có \(x - \pi \; \in D\) và \(x + \pi  \in D\;\)Suy ra \(\begin{array}{l}f\left( {x + \pi } \right) = \cot \left( {x + \pi } \right) = \cot \left( x \right) = f(x)\\f\left( {x - \pi } \right) = \cot \left( {x - \pi } \right) = \cot \left( x \right) = f\left( x \right)\end{array}\)=> Chọn đáp án C

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