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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 11: 4 \sqrt{ \sin\left( x \right) +3 } -1 tìm gtnn gtln

Tháng Bảy 14, 2022 Toán học 1 Comment 0 views

Toán Lớp 11: 4 \sqrt{ \sin\left( x \right) +3 } -1 tìm gtnn gtln

Comments ( 1 )

  1. doanthulan
    doanthulan
    14 Tháng Bảy, 2022 at 10:47 chiều
    Reply
    ~rai~
    \(y=4\sqrt{\sin x+3}-1\\\text{Ta có:}-1\le \sin x\le 1\\\Leftrightarrow 2\le \sin x+3\le 4\\\Leftrightarrow\sqrt{2}\le\sqrt{\sin x+3}\le 2\\\Leftrightarrow 4\sqrt{2}\le 4\sqrt{\sin x+3}\le 8\\\Leftrightarrow 4\sqrt{2}-1\le 4\sqrt{\sin x+3}-1\le 7\\\Leftrightarrow 4\sqrt{2}-1\le y\le 7.\\+)Min_y=4\sqrt{2}-1\Leftrightarrow \sin x=-1\Leftrightarrow x=-\dfrac{\pi}{2}+k\pi.(k\in\mathbb{Z})\\+)Max_y=7\Leftrightarrow \sin x=1\Leftrightarrow x=\dfrac{\pi}{2}+k\pi.(k\in\mathbb{Z})\\\text{Vậy Min}_y=4\sqrt{2}-1\text{ khi }x=-\dfrac{\pi}{2}+k\pi;\\\text{Max}_y=7\text{ khi }x=\dfrac{\pi}{2}+k\pi.(k\in\mathbb{Z})\)

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222-9+11+12:2*14+14 = ? ( )

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