Question

Giúp em làm nhanh câu 3,4 với ạ

Answer 1

3.

\(0\le sin^22x\le1\Rightarrow\dfrac{1+4.0}{5}\le y\le\dfrac{1+4.1}{5}\)

\(\Rightarrow\dfrac{1}{5}\le y\le1\)

\(y_{min}=\dfrac{1}{5}\) khi \(sin2x=0\Rightarrow x=\dfrac{k\pi}{2}\)

\(y_{max}=1\) khi \(cos2x=0\Rightarrow x=\dfrac{\pi}{4}+\dfrac{k\pi}{2}\)

4.

\(y=2sin^2x-\left(1-2sin^2x\right)=4sin^2x-1\)

Do \(0\le sin^2x\le1\Rightarrow-1\le y\le3\)

\(y_{min}=-1\) khi \(sinx=0\Rightarrow x=k\pi\)

\(y_{max}=3\) khi \(cosx=0\Rightarrow x=\dfrac{\pi}{2}+k\pi\)