设函数f(x)=sin(wx+派/3)+sin(wx)(w>0)w为欧密个,相邻两条对称轴间的距离为2,求f(1),若f(x+m)是偶函数,求正数m的最小值
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设函数f(x)=sin(wx+派/3)+sin(wx)(w>0)w为欧密个,相邻两条对称轴间的距离为2,求f(1),若f(x+m)是偶函数,求正数m的最小值
设函数f(x)=sin(wx+派/3)+sin(wx)(w>0)w为欧密个,相邻两条对称轴间的距离为2,求f(1),若f(x+m)是偶函数,求正数m的最小值
设函数f(x)=sin(wx+派/3)+sin(wx)(w>0)w为欧密个,相邻两条对称轴间的距离为2,求f(1),若f(x+m)是偶函数,求正数m的最小值
f(x)=sin(wx+π/3)+sin(wx)
=(3/2)sinwx+(√3/2)coswx
=√3sin(wx+π/6),
相邻两条对称轴间的距离为2,
∴π/w=2,w=π/2.
f(1)=3/2.
f(x+m)是偶函数,
<==>f(x+m)=f(-x+m),
<==>sin[(π/2)(x+m+1/3)]-sin[(π/2)(-x+m+1/3)]=0,
<==>cos[(π/2)(m+1/3)]sin(πx/2)=0对任意x成立,
<==>(π/2)(m+1/3)=(k+1/2)π,k∈Z,
<==>m+1/3=2k+1,
∴正数m的最小值=2/3.
设函数f(x)=sin(wx+派/3)+sin(wx)(w>0)w为欧密个,相邻两条对称轴间的距离为2,求f(1),若f(x+m)是偶函数,求正数m的最小值
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