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

Toán Lớp 11: Tìm GTLN GTNN Y= 2Sin (X-Pi/2)+3 Giúp mình với

Tháng Mười Hai 5, 2022 Toán học 2 Comments 0 views

Toán Lớp 11: Tìm GTLN GTNN Y= 2Sin (X-Pi/2)+3 Giúp mình với

Comments ( 2 )

  1. myngocla
    myngocla
    5 Tháng Mười Hai, 2022 at 9:08 chiều
    Reply
    Ta có:
    -1\le sin(x-\pi/2)\le 1
    <=>-2\le 2sin(x-\pi/2)\le 2
    <=>1\le 2sin(x-\pi/2)+3\le 5
    Hay 1\le y \le 5
    +) miny=1 khi: sin(x-\pi/2)=-1
    <=>x-\pi/2=-\pi/2+k2\pi
    <=>x=k2\pi\ \ (k\in ZZ)
    +) maxy=5 khi: sin(x-\pi/2)=1
    <=>x-\pi/2=\pi/2+k2\pi
    <=>x=\pi+k2\pi\ \ (k\in ZZ)
    Vậy: min y=1; max y=5
     

  2. hoquyly
    hoquyly
    5 Tháng Mười Hai, 2022 at 9:08 chiều
    Reply
    ~rai~
    \(y=2\sin\left(x-\dfrac{\pi}{2}\right)+3\\\quad=2\sin\left[-\left(\dfrac{\pi}{2}-x\right)\right]+3\\\quad=-2\sin\left(\dfrac{\pi}{2}-x\right)+3\\\quad=-2\cos x+3.\\\text{Ta có:}-1\le \cos x\le 1\\\Leftrightarrow -1\le -\cos x\le 1\\\Leftrightarrow -2\le -2\cos x\le 2\\\Leftrightarrow 1\le -2\cos x+3\le 5\\\Leftrightarrow 1\le y\le 5.\\+)\text{Min}_y=1\Leftrightarrow \cos x=1\Leftrightarrow x=k2\pi.(k\in\mathbb{Z})\\+)\text{Max}_y=5\Leftrightarrow \cos x=-1\Leftrightarrow x=\pi+k2\pi.(k\in\mathbb{Z})\\\text{Vậy Min}_y=1\text{ khi }x=k2\pi;\\\text{Max}_y=5\text{ khi }x=\pi+k2\pi.(k\in\mathbb{Z})\)
     

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

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