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来源：学生作业帮助网 编辑：六六作业网 时间：2024/05/06 16:30:17
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t= √2 (√2/2 sinx+√2/2cosx) = √2 sin(x+45°)
- √2≤t≤√2
(2)
f(x)=t+m/2 [ (sinx+ cosx )^2-1]
=t+m/2( t^2-1)
=m/2( t^2 +2/m t-1)
=m/2( t +1/m)^2 - m/2*1/m^2
=m/2( t +1/m)^2 ...
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t= √2 (√2/2 sinx+√2/2cosx) = √2 sin(x+45°)
- √2≤t≤√2
(2)
f(x)=t+m/2 [ (sinx+ cosx )^2-1]
=t+m/2( t^2-1)
=m/2( t^2 +2/m t-1)
=m/2( t +1/m)^2 - m/2*1/m^2
=m/2( t +1/m)^2 - 1 /2m
m≤ - √2/2 或 m ≥ √2/2时
f(x)的最小值为- 1 /2m
- √2/2≤m≤0 时
t= √2，f(x)的最小值为√2+m/2
0≤m≤√2/2时
t= - √2， f(x)的最小值为- √2+m/2
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