Câu hỏi của Lê Minh Hưng

Question

Tìm GTLN, GTNN

a. y= 1+ $\sqrt{2cos^2x+1}$

b. y= 1 + 3sin(2x - $\frac{\pi}{4}$)

c. y= 3 - 2cos23x

d. y= 1 + $\sqrt{2+sin2x}$

e. y= $\frac{4}{2+sin^{2^{ }}x}$

Nguyễn Việt Lâm · Accepted Answer

a.

$0\le cos^2x\le1\Rightarrow2\le y\le1+\sqrt{3}$

$y_{min}=2$ khi $cosx=0$

$y_{max}=1+\sqrt{3}$ khi $cos^2x=1$

b.

$-1\le sin\left(2x-\frac{\pi}{4}\right)\le1\Rightarrow-2\le y\le4$

$y_{min}=-2$ khi $sin\left(2x-\frac{\pi}{4}\right)=-1$

$y_{max}=4$ khi $sin\left(2x-\frac{\pi}{4}\right)=1$

c.

$0\le cos^23x\le1\Rightarrow1\le y\le3$

$y_{min}=1$ khi $cos^23x=1$

$y_{max}=3$ khi $cos3x=0$Câu trả lời: a.

$0\le cos^2x\le1\Rightarrow2\le y\le1+\sqrt{3}$

$y_{min}=2$ khi $cosx=0$

$y_{max}=1+\sqrt{3}$ khi $cos^2x=1$

b.

$-1\le sin\left(2x-\frac{\pi}{4}\right)\le1\Rightarrow-2\le y\le4$

$y_{min}=-2$ khi $sin\left(2x-\frac{\pi}{4}\right)=-1$

$y_{max}=4$ khi $sin\left(2x-\frac{\pi}{4}\right)=1$

c.

$0\le cos^23x\le1\Rightarrow1\le y\le3$

$y_{min}=1$ khi $cos^23x=1$

$y_{max}=3$ khi $cos3x=0$

Nguyễn Việt Lâm · Answer

d.

$-1\le sin2x\le1\Rightarrow2\le y\le1+\sqrt{3}$

$y_{min}=2$ khi $sin2x=-1$

$y_{max}=1+\sqrt{3}$ khi $sin2x=1$

e.

$0\le sin^2x\le1\Rightarrow\frac{4}{3}\le y\le2$

$y_{min}=\frac{4}{3}$ khi $sin^2x=1$

$y_{max}=2$ khi $sinx=0$Câu trả lời: d.

$-1\le sin2x\le1\Rightarrow2\le y\le1+\sqrt{3}$

$y_{min}=2$ khi $sin2x=-1$

$y_{max}=1+\sqrt{3}$ khi $sin2x=1$

e.

$0\le sin^2x\le1\Rightarrow\frac{4}{3}\le y\le2$

$y_{min}=\frac{4}{3}$ khi $sin^2x=1$

$y_{max}=2$ khi $sinx=0$

Bài 1: Hàm số lượng giác