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Giải bài 5.49 trang 90 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Tính \(\mathop {\lim }\limits_{x \to 0} x\sin \frac{1}{x}\).

𓂃Tổng 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

Tính \(\mathop {\lim }\limits_{x \to 0} x\sin \frac{1}{x}\).

Phương pháp giải - Xem chi tiết

Dùng nguyên lý kẹp, chứng minh \(|f({x_n})|\,\, \le \,\,|{x_n}|\,\, \to 0\) từ đó suy ra giới hạn này tiến tới 0.

Lời giải chi tiết

Đặt \(f(x) = x\sin \frac{1}{x}\). Lấy dãy số \(({x_n})\) bất kì thỏa mãn \({x_n} \to 0\).Khi đó \(|f({x_n})|\,\, = \,\,|{x_n}|.\left| {\sin \frac{1}{{{x_n}}}} \right| \le \,\,|{x_n}|\,\, \to 0\).Vậy \(\mathop {\lim }\limits_{x \to 0} f({x_n}) = 0\).

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

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