[Toan 11] 1 số câu trong đề thi hsg trương tui

0

__00changngoc00__

2.
[TEX]\frac{sin2x}{x}=0 [/TEX]
khi x--->-oo
Do [TEX] -1 \leq sin(2x) \leq1[/TEX]
 
N

nhungtihon

lim sin2x/x=lim sin2x.2/2x=2
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N

niemkieuloveahbu

[TEX]\blue \mathbf VP=12+\frac{1}{2}\sin y\leq 12+\frac{1}{2}.1=12,5\\ VT=\frac{1}{2}[1^2+1^2][(cos^2x+\frac{1}{cos^2x})^2+(sin^2x+\frac{1}{sin^2x})^2]\\ \geq \frac{1}{2}[(cos^2x+\frac{1}{cos^2x})^2+(sin^2x+\frac{1}{sin^2x})^2]=\frac{1}{2}[1+\frac{1}{cos^2xsin^2x}]^2\geq \frac{1}{2}[1+\frac{4}{1}]^2=\frac{1}{2}.5^2=12,5\\ Dau\ "="\ \Leftrightarrow \left{siny=1\\cos2x=0\right.\Leftrightarrow \left{x=\frac{\pi}{4}+\frac{n\pi}{2}\\y=\frac{\pi}{2}+2k\pi\right.(k,n \in Z)[/TEX]

Bài sau sử dụng giới hạn kẹp,:)
 
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